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Talk:Part of speech

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Japanese adjectives
READ THIS!

Just in order to keep the editors calm, we know that Japanese does not have, in fact, "two classes of adjectives", but noun-like qualifiers ("na-adjectives") and stative verbs ("i-adjectives"). The "two classes" in the article are a common and very useful simplification. There's definitely a problem with the "correct" view vs. the "traditional" view. IIRC even Japanese language and Japanese grammar contradict each other on this respect. --Pablo D. Flores 12:06, 11 May 2005 (UTC)in other words, there are different speech that is composed by a person

(Old, corrected)
This needs attention badly, but from the start, I think the Japanese examples are nonsense. Someone correct me if I'm wrong, but shinsetsu is a "na-adjective" or a "nominal adjective" or an "adjectival noun" (or whatever), and that doesn't change no matter what particle you put after it, ne? Shinsetsu ni is an adverbial *phrase*, not a word, and ni is an adposition, not a part-of-speech marker! -- Pablo D. Flores 14:01, 10 Dec 2004 (UTC)

This article seems pretty far afield from real liguisting research. For example, the parts of speech listed are pretty Latin-based (most Asian languages, for example, don't have anything that can be reasonably called an "adjective", and most languages do not distinguish adverbs, even European ones). Likewise, I don't think the following sentence is true:

 * In most languages a word can only be one part of speech. English allows some words to play different parts of speech.

For example, "set" can be a noun (such as a set in mathematics), a verb (set it down), or an adjective (the trap is set).

That is, it is clearly true that English words are flexible, and many other languages are less flexible, but I don't think the categroical statement that other languages generally follow the one word/one part of speech rule really holds. --Lee Daniel Crocker

--
 * 2002.03.20: Thank you for that excellent example; I agree with Lee. There is also the confusion of "word" as grapheme (homophones) and "word" as a phonemic item (homonyms), as well as whether we really consider the meanings of "set" above to be the "same word" in any derivational sense, as opposed to different words that are "just pronounced the same".  There certainly are many languages that assign the same phonemic string several different meanings.  For example, the Mandarin Chinese syllable 1yi has approximately 60-ish different possible meanings, depending on context.  Also, almost all languages have productive processes for transforming a morpheme from one lexical class to another - the "verbing" of nouns in English is a good example, as is the "adverb-ing" and "preposition-ing" of certain classes of Mandarin Chinese verbs.  I'd also be careful to distinguish the "schoolmarm grammarian's" definition of English parts of speech from, for example, the lexical classes of Transformational-Generative Grammar.  How to do so in a reasonably clear manner is not for me to undertake 2 hours past my bedtime on a work night.  *grin*  pgdudda

One example of a dodgy part of speech concept is the preposition. It's definition has a word order requirement in it. This results in the need of another part of speech concept postposition, which plays the same role as preposition, but has a different word order requirement.

The situation is anologous to calling an adjective something else if it comes after the noun it qualifies.

Also there may be a case for regarding a preposition/postposition as a different part of speech depending on whether the phrase it heads acts as an adjective, adverb or indirect object.

Is preposition a bona-fide lexical category? Or does P stand for proposition or postposition?

--- User:Karl Palmen

 * 2002.03.21: Hi Karl! Hrmmm...  Yes, it's a "bona-fide" lexical category - I believe linguists use the term "adposition" to cover the set {preposition, postposition}.  But I'm not certain of the terminology, which is why I haven't gone there.  *grin*  I do know that in TGG, the symbol P is used to stand for this syntactic function / lexical category.  The situation is similar to the use of "affix" to cover the set {prefix, suffix, infix} - affixes function similarly across languages, but which of the three subtypes is used varies from language to language.  pgdudda

I'm disambiguating Conjunction, and there is no page on the grammatical sense. Should this link to Grammatical conjunction, or is that phrase not used? If not, is another phrase used, or should we say Conjunction (grammar)? I will leave a link to the disambiguation page for now. — Toby 19:33 Aug 22, 2002 (PDT)

 * A google search turns up only 34 instances of "grammatical conjunction", but it sounds reasonable to me. --Brion

 * Sounds reasonable to me too, but I don't think that we should use it if ordinary linguists and grammarians normally don't. This differs from Logical conjunction and Astronomical conjunction, which I have seen in books. After all, Conjunction (grammar) sounds reasonable too. — Toby 10:55 Aug 24, 2002 (PDT)

Circumpositions
Regarding the addition of circumpositions: it's OK to add them, but the example given in the edit summary is not a circumposition, it's a circumfix. The ge- and -t of gemacht are grammatical bound morphemes. I think the French ne ... pas would qualify as a circumposition. I don't know of any other languages that have them, though, and even in French ne is often deleted when pas follows. --Pablo D. Flores 10:23, 19 May 2005 (UTC)

I apologize for the poor example. I guess I mixed things up. A better example is "von ... aus" as in "_Von_ der Burg _aus_ hast Du einen guten Überblick über die Stadt." (From the castle, you have a good overview over the city.) C.J. 24 May 2005. 17:21 (MEST)

Why "part of speech"?
How did we wind up with this article title? It seems awfully ambiguous for an article title and I don't quite see the problem with using word class. Can someone explain why it should stay under the current title?

Peter Isotalo 16:35, 15 October 2005 (UTC)

 * this may have been written by authors who are not familar with that terminology. i moved to lexical category. perhaps a separate article should be on parts of speech which explains things from a traditional perspective. parts of speech have rather long history which probably cannot be covered adequately in a general article on lexical categories. peace – ishwar  (speak)  23:49, 19 December 2005 (UTC)
 * I have a background in linguistic software, and it was my experience that in 90% of the literature within this domain referred to such as part of speech. I just wanted to point that out, that it is confusing to other audiences with such backgrounds that there is a need to use the name 'lexical category'. It may be more technically appropriate, but it differs from the popular usage in academic articles regarding software. For example, try doing a Google search for part of speech tagging or going to the article Part-of-speech_tagging. I just did a search and it found more than 2 million pages. Just trying to point that out, that linguists seem to have total control over this particular sense of the phrase, and the fact that part of speech redirects here is confusing for others like myself. Perhaps a disambiguation page for Part of speech with a link to lexical category and something along the lines of Part of speech (computing) would help. Since this move was done a year ago and I do not consider myself authoritative I will not make the change, but perhaps it will at least enlighten someone as to yet another interpretation. Josh Froelich 20:43, 29 December 2006 (UTC)
 * Just a quick note about the article title. The main article has been renamed 'lexical category', which I agree with. However, the category page is still 'part of speech' and it of course still links to the article 'part of speech', which then redirects. I am not very well-versed in changing it though, should a change be necessary. —Preceding unsigned comment added by 141.24.80.145 (talk • contribs) 2 July 2007

I have moved the article back to "Part of speech". This is the usual term, much more common than "lexical category". Many of the references given in the article use the term "part of speech". I am missing the justification for the use of the term "lexical category". Try searching Google scholar for "part of speech" vs Google scholar for "lexical category" vs Google scholar for "word class". --Dan Polansky (talk) 19:02, 21 September 2010 (UTC)

Also notice the existence of Category:Parts of speech, created on 31 July 2004. --Dan Polansky (talk) 20:05, 21 September 2010 (UTC)

I feel like it is important to note that when discussing word classes in a linguistic sense, there is a very large difference between part of speech and lexical categories. A lexical category is a class of words that notional content (or physical meaning in the world). This is limited to nouns, verbs, adjectives, adverbs, and sometimes prepositions and pronouns. Other categories that would be considered parts of speech, such as conjunctions, determiners, and auxiliaries, are included in what is known as functional categories, or words/morphological elements that only serve a grammatical purpose. For instance, the word "the" lacks any kind of meaning without the noun it modifies, just as "and" is meaningless outside of its role in connecting phrases. Because these words do not have any meaning in the world and only serve to make the sentence grammatical, they cannot be considered lexical. Therefore, I would suggest that either lexical category be removed from the "also called" section in the beginning paragraph and given a section later on in the article or it be given its own separate page entirely because as it stands it implies a false synonymy. — Preceding unsigned comment added by 68.97.14.99 (talk) 22:35, 10 September 2012 (UTC)

Parts of speech may seem ambiguous but that's because every nation every country and every language has a different way of using language. Each language switches its placement of, for example, nouns and adjectives. §§§§ — Preceding unsigned comment added by Acole511 (talk • contribs) 20:32, 1 November 2016 (UTC)

But I agree that this is about "word classes" and not about "part of speech"! which would be "predicate, subject, object". Correspondingly it links to the German page "Wortart" (type of word) and not to "Satz (Grammatik)" where the functional units of the phrase are discussed. — MFH:Talk 10:00, 3 September 2020 (UTC)

Generative Grammar Lexical Categories
Generative grammar defines lexical categories as 4 possibilities resultant from the binary features [+N] and [+V]. Underthis schema nouns are [+N,-V], verbs [-N,+V], adjective [+N,+V], and prepositions [-N, -V]. There are no lexical categories other than these. With this understanding one can better explain the relationship relationship, such as the fact that both nouns and adjectives require case or for creating more accurate context-sensitive rules such as the of-insertion rule in English where null=> of / [+N]_NP, where NP stands for noun phrase. If possible can the linguists who do the pages considered linguistics stub confirm this and provide a better written and more expansive section?

 * It's true. It's been argued that this way of setting things up are not very insightful, however, and that by such generative grammarians as Mark Baker. Neither 15:53, 18 March 2007 (UTC)

What is it?
I'm a sophomore in college admittedly with poor English skills, but trying to improve. Isn't this supposed to be an encyclopedia? I am not criticizing the poriginal authors of this article, who know much more than I, but I will say that the first sentence of this article contains three words that I, and probably the majority of the population aren't familiar with: 'lexical', 'syntactic' and 'morphological'. I have learned that often the best way to quickly learn a subject in Wiki is to go back to the original article (view history tab) before it became polluted. I applaude the original authors and ask those who are concerned with exacting definitions to remember that approximation is OK early in these articles for the sake of the general public. I am not completely sure but it seems to me that highly educated people (or people who think they are) often try to use WIKI as an archival reference manual, or something to that effect. Wouldn't you agree? —Preceding unsigned comment added by 76.233.66.61 (talk) 13:23, 29 January 2011 (UTC)

Article
To which of those eight word classes do articles belong? --Jobu0101 (talk) 17:33, 22 July 2011 (UTC)

 * In traditional prescriptive English grammar (e.g., what you learn in elementary school), articles are adjectives. In formal linguistics, they are considered determiner, as you could see if you looked in the article before posting your question. r ʨ anaɢ (talk) 22:06, 22 July 2011 (UTC)
 * Thanks. But in formal linguistics you have more than those eight word classes. So what I was looking for is the first part of your answer. I can't find this information in the article. --Jobu0101 (talk) 10:46, 23 July 2011 (UTC)
 * The determiners are given way down, beyond the section on English in the list of open and closed classes. This should be changed so readers don't have a problem finding this information.
 * Demonstratives are suffering the same fate.Kdammers (talk) 09:39, 8 January 2013 (UTC)
 * The claim in this article that articles are "considered by some grammarians to be a type of adjective" is misleading and should be changed.
 * That claim cites the 2014 Oxford Dictionary of English Grammar, which reads, "Some grammarians, even later ones, wrongly considered the articles to be a special kind of adjective" (Note wrongly and considered—past tense). In the following sentence, that article goes on to give an example of such a "later" grammarian, from 1711. Robshpprd (talk) 00:55, 14 March 2022 (UTC)

Historical classes
"defined four main categories of words: [...] These 15 were" looks like a typing error. — Preceding unsigned comment added by 94.209.199.229 (talk) 06:11, 19 November 2013 (UTC)

Numbers - 9th Part of Speech
Indo European langages have the common denominator that there is nine part of speeches. In this article numbers are forgotten. Ex: four, the third, zero etc. If English doesn't count numbers as part of speeches - where do they then belong ? (For instance Hungarian, Finnish, Estonian - languages that not are Indo European, lackes prepositions) Boeing720 (talk) 23:09, 4 December 2013 (UTC)

Answer: going back to very old books on English grammar, we find "noun numeral" being treated as a separate part of speech, same as in Latin ("nomen numerale"). Nowadays, many English grammarists conflate numerals with the parts of speech whose functions they serve: nouns (cardinal numerals, e.g., "one", and collective numerals, e.g., "dozen"), adjectives (ordinal numerals, e.g., "first", and multiplier numerals, e.g., "single") and adverbs (multiplicative numerals, e.g., "once", and distributive numerals, e.g., "singly"). 141.239.243.190 (talk) 09:55, 24 April 2018 (UTC)

What list?
Early on, the article refers to a list of PoS 'above.' There is no list above that statement that I can find. My guess is is that there once was a list with 1.verb, 2. noun etc. that got moved or deleted but the reference to that list got overlooked. Right?211.225.33.104 (talk) 09:45, 30 April 2014 (UTC)

(Nominal) classifiers
The article states that (Indo-?) European don't have nominal classifiers (linguistics. The linked-to article gives at least one example:  head of cattle and the French equivalent (perhaps source).211.225.33.104 (talk) 09:48, 30 April 2014 (UTC)

General Suggestions
I believe that parts of this article could be extended and also more concisely elaborated on. In addition English, it would be helpful to introduce sections on the word classes in other languages. Perhaps there can be a section added to explain the distinction between lexical and grammatical categories. To expand on the paragraph about how certain words in English can fall into multiple categories, it might be helpful to explain how to determine the word class (via tests or clues) if a word has an ambiguous category. Some citations are also missing in the latter half of the article. Cnchia (talk) 02:51, 19 September 2014 (UTC)

 * Ling 300, UBC, right? You all received the assignment to post on a talk page. Interestingly, not one of you has of yet written anything positive about the article you are critiqueing. Criticism is really easy, too easy. --Tjo3ya (talk) 03:34, 19 September 2014 (UTC)

Duplicated information
In this article, half of the information is stated twice. I'm not sure if they're the same or just very similar, but I don't want to accidentally delete information that wasn't actually duplicated.Zombiedude347 (talk) 04:03, 5 November 2014 (UTC)

"Traditional"
What was called "traditional" here, is not traditional. Traditional tems - excluding modern (= degenerative, below simply younger) English terms - are: Notes: -15:10, 26 January 2015 (UTC) — Preceding unsigned comment added by 80.133.123.218 (talk)
 * Latin nomen is either "nomen = nomen substantivum & nomen adjectivum" or "nomen = nomen substantivum & nomen adjectivum & nomen numerale & pronomen & articlus". Same with Latin-German and German terms and most likely with traditional English terms.
 * [] = optional parts of terms
 * = not considered a part of speech
 * {} = not sure whether or not it was/is considered a part of speech, or whether or nor considerations differ
 * ‡¹ German Pronomen and Latin pronoun is what in modern English is known as pronoun and determiner (the later being viewed as a subclass of adjective in modern English)
 * Older English terms can e.g. be found in [books.google.de/books?id=cUcVAAAAQAAJ&pg=PA2] (where it is "noun = noun substantive & noun adjective").
 * There are resp. were many more German terms (e.g. Zwischenwort, Wandelwort).
 * I think "traditional" here is supposed to correspond to what you call "younger". Perhaps it's not the best term, but I can think of anything better to describe it. The point is to distinguish it from the "even younger" modern systems which distinguish things like determiners, complementizers etc. W. P. Uzer (talk) 15:28, 26 January 2015 (UTC)

 * Hey, do you have a source or sources for this table? It looks really nice, and if it's sourced, it could be added to the article. — Eru·tuon 17:30, 26 January 2015 (UTC)
 * I don't know if we necessarily want to fill the article with foreign-language terms for the various parts of speech, unless they have some particular significance (if German, why not also French, Russian, Chinese, etc. etc.?) But certainly we could do with more detailed information about the various listings of parts of speech that have been proposed at various times, and on such things as when and by whom (and in relation to which languages) "noun" came to denote only substantives, etc. W. P. Uzer (talk) 18:57, 26 January 2015 (UTC)
 * Well, including the Greek and Latin terms would be relevant for discussing the etymologies of the English terms, and including the modern German terms, many of which are calques of the Latin terms, would at least be interesting and could be connected to the discussion of how the English terms developed (as transcriptions rather than calques). And we could certainly discuss the terms in other languages, although those that are not related to the Western grammatical tradition would be best placed in another section or article. My perspective is, if we have something to say about the terms in other languages, to compare and contrast them with the English terms etymologically or otherwise, or to compare the grammatical systems they represent with the English grammatical system, they could certainly be included. (Simply listing them, though, would be a little off-topic.) — Eru·tuon 21:26, 26 January 2015 (UTC)

 * Additions:

Though: The same might be true for Dutch, which has terms like "naamwoord" (= nomen) and "zelfstandig naamwoord" & "substantief" (= [nomen] substantivum). Some terms like Eigenschaftswort und Tätigkeitswort don't seem to be translations of Latin terms, but should be new ones, coined by grammarians as they thought it fits better. A source explaining the origin? I don't know any. Like a source, e.g. Schottel's work combined with Gottsched's work combined with some thinking? Schottel should have "beyständiges/beiständiges Nennwort", Gottsched "Beywort/Beiwort". It's obvious that Gottsched's term is a shortening of Schottel's term (though not necessary shortened by Gottsched). -20:28, 28 January 2015 (UTC), 80.133.123.218 — Preceding unsigned comment added by 93.196.237.113 (talk)
 * Older Greek and Latin "linguists" just used 3 terms, which are like "noun", "verb" and "conjunction". Back then adverbs were put next to verbs etc. Older Latin terms: nominatus (~ nomen), vocabulum (~ [nomen] substantivum), convinctio (~ conjunctio), verbum temporale (~ verbum). verbum temporale is still in use (e.g. at la.wiktionary), but maybe it's a modern reinvention.
 * In English there exists (or existed?) the term "nameword" which means the same as "noun" (though I don't know which "noun").
 * Numerals (like "three", "fourth" etc.): Some number words are nomen (like "three", "fourth", "dozen"), but some aren't (like "thrice" which is an adverb). So "nomen numerale" just includes some number words (usually just cardinale numbers (like "three") and ordinal numbers (like "fourth")). Just "numerale" (or "numerus", though that might be rare"), Latin-German "Numerale" and German "Zahlwort" perhaps sometimes include all kinds of number words, though then it's maybe not considered a part of speech.
 * @Eru·tuon:
 * Greek terms are from [logeion.uchicago.edu/index.html] and [www.zeno.org/Pape-1880].
 * Older Latin terms are from [www.zeno.org/Georges-1913], used e.g. by Varro ("De lingua latina") and Quintilian ("De institutione oratoria" or "Institutio oratoria"). Varro's text: [www.thelatinlibrary.com/varro.html] (Latin); translation of Quintilian's text: [penelope.uchicago.edu/Thayer/E/Roman/Texts/Quintilian/Institutio_Oratoria/home.html].
 * Older English terms are e.g. in [books.google.de/books?id=cUcVAAAAQAAJ&pg=PA2], though that is in Early Modern English and "nouns" are written with capital letters like in German, so it's actually Noun Substantive, Article etc. in there.
 * Latin and German terms: They are common in Latin and German. So good grammar books and dictionaries should know them. Some older German terms accompanied by Latin terms can e.g. be found in [www.zeno.org/Literatur/M/Gottsched,+Johann+Christoph/Theoretische+Schriften/Grundlegung+der+deutschen+Sprachkunst/I+Register] (from Gottsched). (Spellings like "Beywort" are dated since around 1900.)
 * @W. P. Uzer:
 * German terms are more like Latin terms (e.g. nomen in contrary to modern English noun). Thus it might help to understand the Latin terms. Also: "Namenwort" is composed like "nameword" (Name=name, Wort=word), so maybe it's somehow related.
 * (Modern) French terms should be more like modern English terms. So (modern) French terms do not help to understand traditional terms; though it maybe influenced the modern English terms and might help to understand them.
 * Chinese terms (most likely) did not influence traditional European terms and most likely did not influence modern English terms.
 * Maybe German, French, Dutch, Chinese, Japanese terms do not belong here - but then they maybe could be mentioned at en.wiktionary, e.g. as an an appendix or wikisaurus like "Names of parts of speech". Than wikipedia could simply refer to wiktionary for foreign terms.
 * -00:51, 27 January 2015 (UTC), 80.133.123.218
 * I guess what I'm looking for is a source that explains the origin of Namenwort, Beiwort, etc. — some of these seem to be calques (loan-translations) of Latin nomen, adjectivum, etc., but a source is needed. Perhaps a German dictionary that has in-depth etymologies would work. — Eru·tuon 17:37, 27 January 2015 (UTC)
 * Some are, like some Latin grammar terms are translations of Greek terms. Latin nomen/Nomen; literal tanslation: Name (= name); German term: Name (rare), Namenwort (Wort = word), Nennwort (from nennen (or from bennenend, Benennung, but then shortened) + Wort). Latin verbum/Verbum (in antique times verbum temporale); literal translation: Wort (resp. zeitliches Wort, die Zeit betreffendes Wort); German term: Zeitwort, also Tätigkeitswort etc.

Adjectives

 * "It was not until later (e.g. Beauzée, 1767) that the adjective was taken as a separate class."

-10:34, 27 January 2015 (UTC)
 * Already Gottsched differed between substantives (nomen substantivum; Hauptwort) and adjectives (nomen adjectivum; Beywort). Though: There substantives and adjectives are both nouns (nomen, Nennwort). ([www.zeno.org/Literatur/M/Gottsched,+Johann+Christoph/Theoretische+Schriften/Grundlegung+der+deutschen+Sprachkunst/I+Register Gottsched's work]) And already Schottel had this kind of distinction. (As far as I remember he used German terms, which are like "selbständiges Nennwort" and "beiständiges Nennwort" (which became shortend to Beiwort), which look more like the Latin terms.)
 * [books.google.de/books?id=C7BeAAAAcAAJ&pg=PA11 Jakob Redinger (1659, Latin & German)] writes that there are 5 flectable parts of speech (nomen [Germ.: Nennwort], adnomen [Germ.: Beinennwort; also Latin adjectivum though just in brackets], pronomen, verbum, participium) and 5 inflectibale parts (adverbium, praepositio, conjunctio, interjectio, adjectio [Germ. Zusazwort ("Zusatzwort")]). There articles are missing, but he's talking about Latin (which has no articles), and there nomen means substantive and adnomen means adjective. His terms most likely were not popular, as it's nowadays like English adjective, Latin-German Adjektiv etc. and not adnoun, Adnomen etc. But anyway, he differed between substantives and adjectives and called them both parts of speech.
 * But none of this contradicts what was written - it just shows that the example given (the 1767 one) was not the most informative, and ought to have been replaced by an earlier one such as Redinger. W. P. Uzer (talk) 13:24, 27 January 2015 (UTC)
 * Well. 1. The statement is kind of misleading. Even though Gottsched (and others) viewed adjectives as a subgroup of noun, adjectives already existed as a separate (sub)class. 2. The statement is kind of unsourced. The ref most likely just proofs that Beauzée viewed adjectives as a separate class (and maybe even a main class and not a subclass), but it most likely doesn't proof that he was the first one to view adjectives as a separate main class. 3. Between Redinger and Beauzée are around 100 years, and maybe before Redinger there were others who viewed adjectives as a main class. -20:39, 28 January 2015 (UTC), 80.133.123.218 — Preceding unsigned comment added by 93.196.237.113 (talk)

Art of Grammar
This is mainly to User:Erutuon: you previously added text and a translation from the Art of Grammar, which leads to a listing of the parts of speech. What I was wondering was whether it goes on to describe the particular parts of speech in the terms given in that section of our article - i.e. do the descriptions given in our text match the original Greek descriptions, as is implied (or are they just some editor's own commentary)? And if they do match, is there a description in the original text for article, which we currently have missing? W. P. Uzer (talk) 11:06, 28 January 2015 (UTC)
 * Here's the section on the article, and my attempt at a translation:
 * ἄρθρον ἐστὶ μέρος λόγου πτωτικόν, προτασσόμενον +καὶ+ ὑποτασσόμενον τῆς κλίσεως τῶν ὀνομάτων. καὶ ἔστι προτακτικὸν μὲν ὁ, ὑποτακτικὸν δὲ ὅς.
 * παρέπεται δὲ αὐτῶι τρία· γένη, ἀριθμοί, πτώσεις.
 * γένη μὲν οὖν εἰσι τρία· ὁ ποιητής, ἡ ποίησις, τὸ ποίημα.
 * ἀριθμοὶ τρεῖς· +ἑνικός+, δυϊκός, πληθυντικός· ἑνικὸς μὲν ὁ ἡ τό, δυϊκὸς δὲ τώ τά +, πληθυντικὸς δὲ οἱ αἱ τά.
 * πτώσεις δὲ ὁ τοῦ τῶι τόν ὦ, +ἡ τῆς τῆι τήν ὦ.
 * "An article is an declinable [inflected, having cases] part of speech, [both] prefixed [arranged before] and suffixed [arranged after, subordinated], with the ending of nouns. And a prefixed one is the [definite article, ], a suffixed one is who [the basic relative pronoun, ].
 * "Three [things] accompany it: classes [genders], numbers, cases.
 * "[There are] three genders: the poet, the poetic composition, the poem [examples of a, a , and a noun].
 * "[There are] three numbers: singular, dual, plural. [The] singular is [the forms of the article], dual is [the  and  forms of the article], and plural is [the  forms of the article].
 * "[The] cases are [ forms of article and the vocative particle O]; [ forms of article and the vocative particle O]."
 * So, it seems to me that the article is not completely accurate: here Dionysius uses the Greek word article (literally, joint) for both what we would call the definite article and what we would call a relative pronoun. (The letters in small caps are abbreviations for the genders, cases, and numbers.)

 * I haven't read enough to be sure whether this is true of other Greek grammarians as well, or whether yet more words would be included under article: for instance, maybe other relative and demonstrative pronouns like οἷος, ὅσος "such as, as many as" (relative pronouns of quality and quantity) and τοῖος, τόσος "this kind, this many" (demonstrative pronouns of quality and quantity). These are related historically and begin with the same sounds as the forms of the relative pronoun and article — . However, unlike the definite article, they could occur without nouns (as independent rather than adjectival pronouns, if that's the correct terminology) in Classical Greek. The definite article was only a pronoun in the Archaic Greek period, for instance in Homeric Greek. So maybe they would be classified in a different category from the article.

 * Synchronically it would make sense to lump the article and relative pronoun together, because they're so similar in form in Ancient Greek, although historically they were distinct: the Greek article came from PIE pronouns beginning in and, and the relative pronoun from an adjectival form beginning in , from the same suffix that gave Greek adjectives in -ιος.  both became Greek  at the beginnings of words, and thus the masculine and feminine nominative singular and plural forms of the article became similar to those of the relative pronoun, though the masculine nominative singular of the relative pronoun has the ending . The rest of the forms of the article begin with  while those of the relative pronoun all begin with . — Eru·tuon 19:03, 28 January 2015 (UTC)

 * I glanced at Dionysius, and in his section on noun he includes the relative and demonstrative pronouns mentioned above (although the demonstrative I mentioned is actually supposed to be τοιοῦτος τοσοῦτος in standard Attic and Koine), as well as interrogatives. That section is much longer, and uses a lot of terms I don't know. The section on pronoun lists only the personal pronouns, reflexive pronouns, and possessive pronominal adjectives: for instance, ἐγώ, ἐμαυτοῦ, and ἐμός. So in Dionysius's terminology, perhaps noun includes typical substantives, adjectives, and most pronouns; pronoun includes the personal, reflexive, and possessive pronouns; and article includes the article and the basic relative pronoun. — Eru·tuon 19:37, 28 January 2015 (UTC)

 * a) E.g. Latin "nomen" can't be translated by modern English "noun", as nomen did include substantives and nouns.
 * b) Maybe older English "pronoun" meant the same as Latin and German "pronomen" and thus it would be something different than modern English "pronoun".
 * c) In Latin there were the terms "articulus praepositivus" and "articulus postpositivus" (Greek: ἄρθρον προτακτικόν (ὁ, ἡ, τό = ho, hē, tó) and ἄρθρον ὑποτακτικόν (ὅς, ἥ, ὅ = hós, hḗ, hó)). So in (older) Latin article had another meaning as well.
 * So grammar terms were/are defined or used differently. Thus: It's either like:
 * A) One can't translate older terms as modern (English) terms mean something different and as newly coined terms do not exist and most likely wouldn't be accepted. E.g.: modern English "noun" means something else than "nomen", and "name" (which would be a literal translation) would be confusing and wouldn't be accepted as a term for the word class.
 * Or
 * B) One can translate older terms with traditional terms, though it could collide with the modern terms, or maybe even translate them with modern terms, but one has to keep in mind that they could be defined differently. E.g.: using "noun" for Latin "nomen" even though it includes substantives (modern English "nouns") and adjectives. "nomen substantive" could then be translated as noun substantive or substantive like it was in traditional usage, or maybe as something like "substantial/essential noun".
 * Maybe one could write something like "attributed to Dionysius Thrax: "Noun":", i.e. putting quotation marks around the terms to imply that the term is used differently from the modern usage.
 * PS: In case of the Greek articulus postpositivus = the relative pronoun: Maybe one could simple call it a different classification of a single word. Modern Exemple: The classification of German "selbst" is ambiguous. Some (German) dictionaries label it a particle (Partikel), some a pronoun (Pronomen). But there's no question, what "Pronomen" means.
 * -93.196.237.113 (talk) 21:21, 28 January 2015 (UTC)
 * Thanks for the information. I made a quick update to the article on the basis of it. Someone might like to incorporate more of the detail. W. P. Uzer (talk) 14:37, 29 January 2015 (UTC)

Because of "Article (árthron): a declinable part of speech, taken to include the definite article, but also the basic relative pronoun":

I've just read in (younger) grammar book that in old Greek terms the interrogative pronouns and indefinite pronouns were part of the "noun (ónoma)" and not of the "pronoun (antōnymía)". So there are other differences as well, and thus it might be better to omit such differences resp. to just note that these classes sometimes differ from modern understandings. -91.63.231.162 (talk) 21:22, 15 June 2015 (UTC)

Aristoteles
"Aristotle added another class, "conjunctions" [sýndesmos], which included not only the words known today as conjunctions, but also pronouns, prepositions, and the article." There's a reference for that, but that's more than questionable: Thus: Correctly it's most likely that there are different interpretations of Aristoteles' terms, some that it's this way, some others say it's that way. So the best way should be to write something like "There are different interpretations of Aristoteles' terms. Some that it's this way, some others say it's that way." in the article.
 * [books.google.de/books?id=hkJCAQAAMAAJ] (p.176) states that Aristoteles' conjunction means particle, that are words which can not be inflected. So it would include adverb, interjection, preposition, conjunction, but not pronoun and not article (at least in Greek and German, not in English and maybe in other Romance languages).
 * [archive.org/stream/onlatinlanguage02varruoft#page/378/mode/2up] (+ the following page), Varro's "De lingua latina" with a translation as "On the Latin Language":
 * First it is: "In the word-classes in which inflections may develop, the parts of speech are two, unless, following Dion, we divide into three divisions the ideas which are indicated by words: one division which indicates also case, a second which indicates also time, a third which indicates neither. Of these, Aristotle says that there are two parts of speech; nouns, like homo 'man' and equus 'horse', and verbs like legit 'gathers' and currit 'runs'." That sounds like: noun (vocabulum/nomen) = noun substantive, noun adjective, numeral, pronoun, participle, article (in Greek and German, not in Latin and English); verb (verbum) = verb; conjunction (conjunctio/convinctio) = adverb, interjection, conjunction, preposition.
 * Though than it is: "Of the two kinds, noun and verbs, certain words are primary and certain are secondary: primary like homo 'man' and scribit 'writes', and secondary like doctus 'learned' and docte 'learnedly', for we say homo doctos 'a learned man' and scribit docte 'writes learnedly'. These ideas are attended by those of place and time, because neither homo nor scribit can be asserted without the presupposition of place and of time -- yet in such a way that place is more closely associated with the idea of the noun homo, and time more closely with the act of writing." That sounds like noun includes noun substantives and noun adjectives (but could also include the other words with cases), but that may also sound like verb includes both verbs and adverbs.
 * In [penelope.uchicago.edu/Thayer/E/Roman/Texts/Quintilian/Institutio_Oratoria/1B*.html] it's: "18 Earlier writers, among them Aristotle himself and Theodectes, hold that there are but three, verbs, nouns and convinctions. Their view was that the force of language resided in the verbs, and the matter in the nouns (for the one is what we speak, the other that which we speak about), while the duty of the convinctions was to provide a link between the nouns and the verbs. I know that conjunction is the term in general use. But convinction seems to me to be the more accurate translation of the Greek συνδεσμός. 19 Gradually the number was increased by the philosophers, more especially by the Stoics: articles were first added to the convinctions, then prepositions: to nouns appellations were added, then the pronoun and finally the participle, which holds a middle position between the verb and the noun. To the verb itself was added the adverb. Our own language dispenses with the articles, which are therefore distributed among the other parts of speech. 20 But interjections must be added to those already mentioned.". That sounds like: noun includes noun substantive, noun adjective, numeral, pronoun, participle; verb includes verb, adverb; conjunction includes conjunction, preposition, article.
 * Interjection might either belong to the verb (as it was part of the adverb in Dionysius Thrax Techne Grammatike) or to the conjunction (as interjections are particles, not flectable words, like conjunctions and prepositions).
 * It might be that "article" includes both articulus praepositivus and articulus postpositivus (which is viewed as a relative pronoun in modern times). But then, saying that "pronouns are part of the conjunction" is wrong anyway. Correctly that would be, if article includes both types of article, "some pronouns are part of the noun, while some are part of the conjunction". [Also see the PS.]
 * BTW: Later in the text it is said that some say that noun includes proper nouns and appellative nouns (common nouns), while some others say that there are "propers" and "appellatives" (adding noun to them here would be misleading). The common variant should be similar to the modern one: noun is either abstract or concrete, the concrete is proper or appellative (common), or maybe also collective or material (some add the collective and material noun to concrete noun, while others add it to appellative).

PS - might also relate to the above discussion and to the following statements in the article: "Article (árthron): a declinable part of speech, taken to include the definite article, but also the basic relative pronoun" and "The Latin grammarian Priscian (fl. 500 AD) modified the above eightfold system, excluding "article"". Isn't the Latin "qui, quae, quod" the basic relative pronoun of Latin? So: In case of Greek "article" and "pronoun" might mean something different in antique times than they mean nowadays, but in case of Latin they mean the same: Quintilian and Priscian exclude the article from Latin, but they don't exclude the Latin relative pronoun. -02:59, 24 March 2015 (UTC), PS: 04:48, 24 March 2015 (UTC)

VANDALISM
The introduction has been vandalized to the extent it makes no sense. It is more than just the last edit. Some-body please clean it up. Kdammers (talk) 16:50, 31 January 2016 (UTC)

Adverbs
Perhaps a thorough explanation of the difference between adverbs and adjectives would help. Parts of speech can sometimes get confusing especially with adverbs and adjectives. — Preceding unsigned comment added by Boorumr (talk • contribs) 18:56, 1 November 2016 (UTC)

"instead are the noun they refer to bent": ??
Original context in lede:

 * Uralic languages like Finnish and Hungarian lacks prepositions (instead are the noun they refer to bent), a very significant difference.

I have no clue what this phrase means in standard English. Help? --Pete Tillman (talk) 20:29, 16 July 2017 (UTC)
 * @Pete Tillman: My guess is that they intended to say that, instead of adding a preposition before a noun to achieve an effect, the noun is inflected ("bent") to achieve the same effect. Thus, for English and Czech: "I gave the cup to Peter" would be rendered as Czech "Hrnek jsem dal Petrovi"; here, English uses preposition "to" for an effect that is achieved in Czech by inflecting the noun "Petr" to yield "Petrovi". Just a guess. --Dan Polansky (talk) 15:38, 22 July 2018 (UTC)

 * Thanks. Gone now. No time at the moment to look further, sorry. Cheers, Pete Tillman (talk) 23:47, 22 July 2018 (UTC)

Will pronouns remain a closed class, or will they open?
It is noted that pronouns remain a closed class (a class of words rarely if ever added to), but now with the sudden affection of "76 genders" and asking "what your pronouns are", will that remain true? There should be a section mentioning pronouns will become an open class with designer genders. 174.114.77.231 (talk) 02:09, 9 October 2017 (UTC)

Participles and gerunds/verbal nouns
The page does not currently say where participles and gerunds (or verbal nouns in some languages) fit. These kinds of words are somewhat ambiguous. Participles are traditionally considered verb forms, and have some properties typically associated with verbs. Yet they can also modify nouns like adjectives (e.g. a falling tree), and in many languages such as German, they inflect like adjectives too. The same question applies to gerunds or verbal nouns as well. While they have verbal properties, such as taking objects, they inflect like nouns in some languages and can also have grammatical gender.

How do POS/lexical category classifications figure in these cases? Do they consider them verbs, or nouns and adjectives? Does their part of speech depend on how they are used, with some uses being verbal and others being adjectival/nominal? Or could they even be given their own label, separate from all of these, to accurately encompass both the verbal and adjectival/nominal properties? Rua (mew) 11:14, 25 April 2019 (UTC)

English
He is the tallest Man in the world 144.48.132.233 (talk) 16:34, 23 February 2023 (UTC)

parts of speech
in the mend department we bought tied shirts and socks 2600:6C58:47F:BDD6:30AB:8BDB:2FE9:F3DE (talk) 20:50, 16 January 2024 (UTC)

title: Talk:Part of speech


text:
Negative binomial distribution

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted $$r$$) occurs. For example, we can define rolling a 6 on some dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ($$r=3$$). In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution.

An alternative formulation is to model the number of total trials (instead of the number of failures). In fact, for a specified (non-random) number of successes (r), the number of failures (n − r) is random because the number of total trials (n) is random. For example, we could use the negative binomial distribution to model the number of days n (random) a certain machine works (specified by r) before it breaks down.

The Pascal distribution (after Blaise Pascal) and Polya distribution (for George Pólya) are special cases of the negative binomial distribution. A convention among engineers, climatologists, and others is to use "negative binomial" or "Pascal" for the case of an integer-valued stopping-time parameter ($$r$$) and use "Polya" for the real-valued case.

For occurrences of associated discrete events, like tornado outbreaks, the Polya distributions can be used to give more accurate models than the Poisson distribution by allowing the mean and variance to be different, unlike the Poisson. The negative binomial distribution has a variance $$\mu /p$$, with the distribution becoming identical to Poisson in the limit $$p\to 1$$ for a given mean $$\mu$$ (i.e. when the failures are increasingly rare). This can make the distribution a useful overdispersed alternative to the Poisson distribution, for example for a robust modification of Poisson regression. In epidemiology, it has been used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. More generally, it may be appropriate where events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term.

The term "negative binomial" is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability mass function of the distribution can be written more simply with negative numbers.

Definitions
Imagine a sequence of independent Bernoulli trials: each trial has two potential outcomes called "success" and "failure." In each trial the probability of success is $$p$$ and of failure is $$1-p$$. We observe this sequence until a predefined number $$r$$ of successes occurs. Then the random number of observed failures, $$X$$, follows the negative binomial (or Pascal) distribution:

X\sim\operatorname{NB}(r, p) $$

Probability mass function
The probability mass function of the negative binomial distribution is

f(k; r, p) \equiv \Pr(X = k) = \binom{k+r-1}{k} (1-p)^k p^r $$

where r is the number of successes, k is the number of failures, and p is the probability of success on each trial.

Here, the quantity in parentheses is the binomial coefficient, and is equal to

\binom{k+r-1}{k} = \frac{(k+r-1)!}{(r-1)!\,(k)!} = \frac{(k+r-1)(k+r-2)\dotsm(r)}{k!} = \frac{\Gamma(k + r)}{k!\ \Gamma(r)}. $$ Note that Γ(r) is the Gamma function.

There are k failures chosen from k + r − 1 trials rather than k + r because the last of the k + r trials is by definition a success.

This quantity can alternatively be written in the following manner, explaining the name "negative binomial":

\begin{align} & \frac{(k+r-1)\dotsm(r)}{k!} \\[10pt] = {} & (-1)^k \frac{\overbrace{(-r)(-r-1)(-r-2)\dotsm(-r-k+1)}^{k\text{ factors}}}{k!} = (-1)^k\binom{-r}{\phantom{-}k}. \end{align} $$

Note that by the last expression and the binomial series, for every 0 ≤ p < 1 and $$q=1-p$$,

p^{-r} = (1-q)^{-r} = \sum_{k=0}^\infty \binom{-r}{\phantom{-}k}(-q)^k = \sum_{k=0}^\infty \binom{k+r-1}{k}q^k $$

hence the terms of the probability mass function indeed add up to one as below.

\sum_{k=0}^\infty \binom{k+r-1}{k}(1-p)^kp^r = p^{-r}p^r = 1 $$

To understand the above definition of the probability mass function, note that the probability for every specific sequence of r successes and k failures is pr(1 − p)k, because the outcomes of the k + r trials are supposed to happen independently. Since the rth success always comes last, it remains to choose the k trials with failures out of the remaining k + r − 1 trials. The above binomial coefficient, due to its combinatorial interpretation, gives precisely the number of all these sequences of length k + r − 1.

Cumulative distribution function
The cumulative distribution function can be expressed in terms of the regularized incomplete beta function:

F(k; r, p) \equiv \Pr(X\le k) = I_{p}(r, k+1). $$ (This formula is using the same parameterization as in the article's table, with r the number of successes, and $$p=r/(r+\mu)$$ with $$\mu$$ the mean.)

It can also be expressed in terms of the cumulative distribution function of the binomial distribution:

F(k; r, p) = F_\text{binomial}(k;n=k+r,1-p). $$

Alternative formulations
Some sources may define the negative binomial distribution slightly differently from the primary one here. The most common variations are where the random variable X is counting different things. These variations can be seen in the table here: Each of the four definitions of the negative binomial distribution can be expressed in slightly different but equivalent ways. The first alternative formulation is simply an equivalent form of the binomial coefficient, that is: $ \binom ab = \binom a{a-b} \quad \text{for }\ 0\leq b\leq a$. The second alternate formulation somewhat simplifies the expression by recognizing that the total number of trials is simply the number of successes and failures, that is: $n=r+k $ . These second formulations may be more intuitive to understand, however they are perhaps less practical as they have more terms.
 * The definition where X is the number of n trials that occur for a given number of r successes is similar to the primary definition, except that the number of trials is given instead of the number of failures. This adds r to the value of the random variable, shifting its support and mean.
 * The definition where X is the number of k successes (or n trials) that occur for a given number of r failures is similar to the primary definition used in this article, except that numbers of failures and successes are switched when considering what is being counted and what is given. Note however, that p still refers to the probability of "success".
 * The definition of the negative binomial distribution can be extended to the case where the parameter r can take on a positive real value. Although it is impossible to visualize a non-integer number of "failures", we can still formally define the distribution through its probability mass function.  The problem of extending the definition to real-valued (positive) r boils down to extending the binomial coefficient to its real-valued counterpart, based on the gamma function:

\binom{k+r-1}{k} = \frac{(k+r-1)(k+r-2)\dotsm(r)}{k!} = \frac{\Gamma(k+r)}{k!\,\Gamma(r)} $$
 * After substituting this expression in the original definition, we say that X has a negative binomial (or Pólya) distribution if it has a probability mass function:

f(k; r, p) \equiv \Pr(X = k) = \frac{\Gamma(k+r)}{k!\,\Gamma(r)} (1-p)^k p^r \quad\text{for }k = 0, 1, 2, \dotsc $$
 * Here r is a real, positive number.

In negative binomial regression, the distribution is specified in terms of its mean, $m=\frac{r(1-p)}{p}$, which is then related to explanatory variables as in linear regression or other generalized linear models. From the expression for the mean m, one can derive $p=\frac{r}{m+r}$ and $1-p=\frac{m}{m+r}$. Then, substituting these expressions in the one for the probability mass function when r is real-valued, yields this parametrization of the probability mass function in terms of m:

\Pr(X = k) = \frac{\Gamma(r+k)}{k! \, \Gamma(r)} \left(\frac{r}{r+m}\right)^r \left(\frac{m}{r+m}\right)^k \quad\text{for }k = 0, 1, 2, \dotsc $$ The variance can then be written as $m+\frac{m^2}{r}$. Some authors prefer to set $\alpha = \frac{1}{r}$, and express the variance as $m+\alpha m^2$. In this context, and depending on the author, either the parameter r or its reciprocal α is referred to as the "dispersion parameter", "shape parameter" or "clustering coefficient", or the "heterogeneity" or "aggregation" parameter. The term "aggregation" is particularly used in ecology when describing counts of individual organisms. Decrease of the aggregation parameter r towards zero corresponds to increasing aggregation of the organisms; increase of r towards infinity corresponds to absence of aggregation, as can be described by Poisson regression.

Alternative parameterizations
Sometimes the distribution is parameterized in terms of its mean μ and variance σ2:

\begin{align} & p =\frac{\mu}{\sigma^2}, \\[6pt] & r =\frac{\mu^2}{\sigma^2-\mu}, \\[3pt] & \Pr(X=k) = {k+\frac{\mu^2}{\sigma^2-\mu}-1 \choose k} \left(1-\frac{\mu}{\sigma^2}\right)^k \left(\frac \mu {\sigma^2}\right)^{\mu^2/(\sigma^2-\mu)} \\ & \operatorname{E}(X) = \mu \\ & \operatorname{Var}(X) = \sigma^2. \end{align} $$

Another popular parameterization uses r and the failure odds β:

\begin{align} & p = \frac{1}{1+\beta} \\ & \Pr(X=k) = {k+r-1 \choose k} \left(\frac{\beta}{1+\beta}\right)^k \left(\frac {1} {1+\beta}\right)^r \\ & \operatorname{E}(X) = r\beta \\ & \operatorname{Var}(X) = r\beta(1+\beta). \end{align} $$

Length of hospital stay
Hospital length of stay is an example of real-world data that can be modelled well with a negative binomial distribution via negative binomial regression.

Selling candy
Pat Collis is required to sell candy bars to raise money for the 6th grade field trip. Pat is (somewhat harshly) not supposed to return home until five candy bars have been sold. So the child goes door to door, selling candy bars. At each house, there is a 0.6 probability of selling one candy bar and a 0.4 probability of selling nothing.

What's the probability of selling the last candy bar at the nth house?

Successfully selling candy enough times is what defines our stopping criterion (as opposed to failing to sell it), so k in this case represents the number of failures and r represents the number of successes. Recall that the NegBin(r, p) distribution describes the probability of k failures and r successes in k + r Bernoulli(p) trials with success on the last trial. Selling five candy bars means getting five successes. The number of trials (i.e. houses) this takes is therefore k + 5 = n. The random variable we are interested in is the number of houses, so we substitute k = n − 5 into a NegBin(5, 0.4) mass function and obtain the following mass function of the distribution of houses (for n ≥ 5):

 * $$ f(n) = {(n-5) + 5 - 1 \choose n-5} \; (1-0.4)^5 \; 0.4^{n-5} = {n-1 \choose n-5} \; 3^5 \; \frac{2^{n-5}}{5^n}. $$

What's the probability that Pat finishes on the tenth house?

 * $$ f(10) = 0.1003290624. \, $$

What's the probability that Pat finishes on or before reaching the eighth house?

To finish on or before the eighth house, Pat must finish at the fifth, sixth, seventh, or eighth house. Sum those probabilities:
 * $$ f(5) = 0.07776 \, $$
 * $$ f(6) = 0.15552 \, $$
 * $$ f(7) = 0.18662 \, $$
 * $$ f(8) = 0.17418 \, $$
 * $$\sum_{j=5}^8 f(j) = 0.59408.$$

What's the probability that Pat exhausts all 30 houses that happen to stand in the neighborhood?

This can be expressed as the probability that Pat does not finish on the fifth through the thirtieth house:
 * $$1-\sum_{j=5}^{30} f(j) = 1 - I_{0.4}(5, 30-5+1) \approx 1 - 0.99999342 = 0.00000658. $$

Because of the rather high probability that Pat will sell to each house (60 percent), the probability of her NOT fulfilling her quest is vanishingly slim.

Expectation
The expected total number of trials needed to see r successes is $$\frac{r}{p}$$. Thus, the expected number of failures would be this value, minus the successes:

E[\operatorname{NB}(r, p)] = \frac{r}{p} - r = \frac{r(1-p)}{p} $$

Expectation of successes
The expected total number of failures in a negative binomial distribution with parameters $(r, p)$ is r(1 − p)/p. To see this, imagine an experiment simulating the negative binomial is performed many times. That is, a set of trials is performed until $r$ successes are obtained, then another set of trials, and then another etc. Write down the number of trials performed in each experiment: $a, b, c, ...$ and set $a + b + c + ... = N$. Now we would expect about $Np$ successes in total. Say the experiment was performed $n$ times. Then there are $nr$ successes in total. So we would expect $nr = Np$, so $N/n = r/p$. See that $N/n$ is just the average number of trials per experiment. That is what we mean by "expectation". The average number of failures per experiment is $N/n − r = r/p − r = r(1 − p)/p$. This agrees with the mean given in the box on the right-hand side of this page.

A rigorous derivation can be done by representing the negative binomial distribution as the sum of waiting times. Let $$X_r \sim\operatorname{NB}(r, p)$$ with the convention $$X$$ represents the number of failures observed before $$r$$ successes with the probability of success being $$p$$. And let $$Y_i \sim Geom(p)$$ where $$Y_i$$ represents the number of failures before seeing a success. We can think of $$Y_i$$ as the waiting time (number of failures) between the $$i$$th and $$(i-1)$$th success. Thus

X_r = Y_1 + Y_2 + \cdots + Y_r. $$ The mean is

E[X_r] = E[Y_1] + E[Y_2] + \cdots + E[Y_r] = \frac{r(1-p)}{p}, $$ which follows from the fact $$E[Y_i] = (1-p)/p$$.

Variance
When counting the number of failures before the r-th success, the variance is r(1 − p)/p2. When counting the number of successes before the r-th failure, as in alternative formulation (3) above, the variance is rp/(1 − p)2.

Relation to the binomial theorem
Suppose Y is a random variable with a binomial distribution with parameters n and p. Assume p + q = 1, with p, q ≥ 0, then

 * $$1=1^n=(p+q)^n.$$

Using Newton's binomial theorem, this can equally be written as:

 * $$(p+q)^n=\sum_{k=0}^\infty {n \choose k} p^k q^{n-k},$$

in which the upper bound of summation is infinite. In this case, the binomial coefficient

 * $${n \choose k}={n(n-1)(n-2)\cdots(n-k+1) \over k! }.$$

is defined when n is a real number, instead of just a positive integer. But in our case of the binomial distribution it is zero when k > n. We can then say, for example

 * $$(p+q)^{8.3}=\sum_{k=0}^\infty {8.3 \choose k} p^k q^{8.3 - k}.$$

Now suppose r > 0 and we use a negative exponent:

 * $$1=p^r\cdot p^{-r}=p^r (1-q)^{-r}=p^r \sum_{k=0}^\infty {-r \choose k} (-q)^k.$$

Then all of the terms are positive, and the term

 * $$p^r {-r \choose k} (-q)^k$$

is just the probability that the number of failures before the rth success is equal to k, provided r is an integer. (If r is a negative non-integer, so that the exponent is a positive non-integer, then some of the terms in the sum above are negative, so we do not have a probability distribution on the set of all nonnegative integers.)

Now we also allow non-integer values of r. Then we have a proper negative binomial distribution, which is a generalization of the Pascal distribution, which coincides with the Pascal distribution when r happens to be a positive integer.

Recall from above that

 * The sum of independent negative-binomially distributed random variables r1 and r2 with the same value for parameter p is negative-binomially distributed with the same p but with r-value r1 + r2.

This property persists when the definition is thus generalized, and affords a quick way to see that the negative binomial distribution is infinitely divisible.

Recurrence relations
The following recurrence relations hold:

For the probability mass function
 * $$ \begin{cases}

(k+1) \Pr (X=k+1)-p \Pr (X=k) (k+r)=0, \\[5pt] \Pr (X=0)=(1-p)^r. \end{cases} $$

For the moments $$m_k = \mathbb E(X^k),$$
 * $$ m_{k+1} = r P m_k + (P^2 + P) {d m_k \over dP}, \quad P:=(1-p)/p, \quad m_0=1.

$$

For the cumulants
 * $$ \kappa_{k+1} = (Q-1)Q {d \kappa_k \over dQ}, \quad Q:=1/p, \quad \kappa_1=r(Q-1).

$$

Related distributions

 * The geometric distribution (on { 0, 1, 2, 3, ... }) is a special case of the negative binomial distribution, with
 * $$\operatorname{Geom}(p) = \operatorname{NB}(1,\, p).\,$$

 * The negative binomial distribution is a special case of the discrete phase-type distribution.
 * The negative binomial distribution is a special case of discrete compound Poisson distribution.

Poisson distribution
Consider a sequence of negative binomial random variables where the stopping parameter r goes to infinity, while the probability p of success in each trial goes to one, in such a way as to keep the mean of the distribution (i.e. the expected number of failures) constant. Denoting this mean as λ, the parameter p will be p = r/(r + λ)

\begin{align} \text{Mean:} \quad & \lambda = \frac{(1-p)r}{p} \quad \Rightarrow \quad p = \frac{r}{r+\lambda}, \\ \text{Variance:} \quad & \lambda \left( 1 + \frac{\lambda}{r} \right) > \lambda, \quad \text{thus always overdispersed}. \end{align} $$

Under this parametrization the probability mass function will be

f(k; r, p) = \frac{\Gamma(k+r)}{k!\cdot\Gamma(r)}(1-p)^k p^r = \frac{\lambda^k}{k!} \cdot \frac{\Gamma(r+k)}{\Gamma(r)\;(r+\lambda)^k} \cdot \frac{1}{\left(1+\frac{\lambda}{r}\right)^r} $$

Now if we consider the limit as r → ∞, the second factor will converge to one, and the third to the exponent function:

\lim_{r\to\infty} f(k; r, p) = \frac{\lambda^k}{k!} \cdot 1 \cdot \frac{1}{e^\lambda}, $$ which is the mass function of a Poisson-distributed random variable with expected value λ.

In other words, the alternatively parameterized negative binomial distribution converges to the Poisson distribution and r controls the deviation from the Poisson. This makes the negative binomial distribution suitable as a robust alternative to the Poisson, which approaches the Poisson for large r, but which has larger variance than the Poisson for small r.

\operatorname{Poisson}(\lambda) = \lim_{r \to \infty} \operatorname{NB} \left(r, \frac{r}{r + \lambda}\right). $$

Gamma–Poisson mixture
The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a Poisson(λ) distribution, where λ is itself a random variable, distributed as a gamma distribution with shape r and scale  θ =(1 − p)/p or correspondingly rate β =p/(1 − p).

To display the intuition behind this statement, consider two independent Poisson processes, "Success" and "Failure", with intensities p and 1 − p. Together, the Success and Failure processes are equivalent to a single Poisson process of intensity 1, where an occurrence of the process is a success if a corresponding independent coin toss comes up heads with probability p; otherwise, it is a failure. If r is a counting number, the coin tosses show that the count of successes before the rth failure follows a negative binomial distribution with parameters r and p. The count is also, however, the count of the Success Poisson process at the random time T of the rth occurrence in the Failure Poisson process. The Success count follows a Poisson distribution with mean pT, where T is the waiting time for r occurrences in a Poisson process of intensity 1 − p, i.e., T is gamma-distributed with shape parameter r and intensity 1 − p. Thus, the negative binomial distribution is equivalent to a Poisson distribution with mean pT, where the random variate T is gamma-distributed with shape parameter r and intensity (1 − p). The preceding paragraph follows, because λ = pT is gamma-distributed with shape parameter r and intensity (1 − p)/p.

The following formal derivation (which does not depend on r being a counting number) confirms the intuition.

 * $$\begin{align}

& \int_0^\infty f_{\operatorname{Poisson}(\lambda)}(k) \times f_{\operatorname{Gamma}\left(r,\, \frac{p}{1-p}\right)}(\lambda) \, \mathrm{d}\lambda \\[8pt] = {} & \int_0^\infty \frac{\lambda^k}{k!} e^{-\lambda} \times \frac 1 {\Gamma(r)} \left(\frac{p}{1-p} \lambda \right)^{r-1} e^{- \frac{p}{1-p} \lambda} \, \left( \frac p{1-p} \, \right)\mathrm{d}\lambda \\[8pt] = {} & \left(\frac{p}{1-p}\right)^r \frac{1}{k!\,\Gamma(r)} \int_0^\infty \lambda^{r+k-1} e^{-\lambda \frac{p+1-p}{1-p}} \;\mathrm{d}\lambda \\[8pt] = {} & \left(\frac{p}{1-p}\right)^r \frac{1}{k!\,\Gamma(r)} \Gamma(r+k) (1-p)^{k+r} \int_0^\infty f_{\operatorname{Gamma}\left(k+r, \frac{1}{1-p}\right)}(\lambda) \;\mathrm{d}\lambda \\[8pt] = {} & \frac{\Gamma(r+k)}{k!\;\Gamma(r)} \; (1-p)^k \,p^r \\[8pt] = {} & f(k; r, p). \end{align}$$

Because of this, the negative binomial distribution is also known as the gamma–Poisson (mixture) distribution. The negative binomial distribution was originally derived as a limiting case of the gamma-Poisson distribution.

Distribution of a sum of geometrically distributed random variables
If Yr is a random variable following the negative binomial distribution with parameters r and p, and support {0, 1, 2, ...}, then Yr is a sum of r independent variables following the geometric distribution (on {0, 1, 2, ...}) with parameter p. As a result of the central limit theorem, Yr (properly scaled and shifted) is therefore approximately normal for sufficiently large r.

Furthermore, if Bs+r is a random variable following the binomial distribution with parameters s + r and p, then

\begin{align} \Pr(Y_r \leq s) & {} = 1 - I_p(s+1, r) \\[5pt] & {} = 1 - I_{p}((s+r)-(r-1), (r-1)+1) \\[5pt] & {} = 1 - \Pr(B_{s+r} \leq r-1) \\[5pt] & {} = \Pr(B_{s+r} \geq r) \\[5pt] & {} = \Pr(\text{after } s+r \text{ trials, there are at least } r \text{ successes}). \end{align} $$

In this sense, the negative binomial distribution is the "inverse" of the binomial distribution.

The sum of independent negative-binomially distributed random variables r1 and r2 with the same value for parameter p is negative-binomially distributed with the same p but with r-value r1 + r2.

The negative binomial distribution is infinitely divisible, i.e., if Y has a negative binomial distribution, then for any positive integer n, there exist independent identically distributed random variables Y1, ..., Yn whose sum has the same distribution that Y has.

Representation as compound Poisson distribution
The negative binomial distribution NB(r,p) can be represented as a compound Poisson distribution: Let $ (Y_n)_{n\,\in\,\mathbb N} $ denote a sequence of independent and identically distributed random variables, each one having the logarithmic series distribution Log(p), with probability mass function

 * $$ f(k; r, p) = \frac{-p^k}{k\ln(1-p)},\qquad k\in{\mathbb N}.$$

Let N be a random variable, independent of the sequence, and suppose that N has a Poisson distribution with mean. Then the random sum

 * $$X=\sum_{n=1}^N Y_n$$

is NB(r,p)-distributed. To prove this, we calculate the probability generating function GX of X, which is the composition of the probability generating functions GN and GY 1. Using

 * $$G_N(z)=\exp(\lambda(z-1)),\qquad z\in\mathbb{R},$$

and

 * $$G_{Y_1}(z)=\frac{\ln(1-pz)}{\ln(1-p)},\qquad |z|<\frac1p,$$

we obtain

\begin{align}G_X(z) & =G_N(G_{Y_1}(z))\\[4pt] &=\exp\biggl(\lambda\biggl(\frac{\ln(1-pz)}{\ln(1-p)}-1\biggr)\biggr)\\[4pt] &=\exp\bigl(-r(\ln(1-pz)-\ln(1-p))\bigr)\\[4pt] &=\biggl(\frac{1-p}{1-pz}\biggr)^r,\qquad |z|<\frac1p, \end{align} $$

which is the probability generating function of the NB(r,p) distribution.

The following table describes four distributions related to the number of successes in a sequence of draws:

(a,b,0) class of distributions
The negative binomial, along with the Poisson and binomial distributions, is a member of the (a,b,0) class of distributions. All three of these distributions are special cases of the Panjer distribution. They are also members of a natural exponential family.

MVUE for p
Suppose p is unknown and an experiment is conducted where it is decided ahead of time that sampling will continue until r successes are found. A sufficient statistic for the experiment is k, the number of failures.

In estimating p, the minimum variance unbiased estimator is

 * $$\widehat{p}=\frac{r-1}{r+k-1}.$$

Maximum likelihood estimation
When r is known, the maximum likelihood estimate of p is

 * $$\widetilde{p}=\frac{r}{r+k},$$

but this is a biased estimate. Its inverse (r + k)/r, is an unbiased estimate of 1/p, however.

When r is unknown, the maximum likelihood estimator for p and r together only exists for samples for which the sample variance is larger than the sample mean. The likelihood function for N iid observations (k1, ..., kN) is

 * $$L(r,p)=\prod_{i=1}^N f(k_i;r,p)\,\!$$

from which we calculate the log-likelihood function

 * $$\ell(r,p) = \sum_{i=1}^N \ln(\Gamma(k_i + r)) - \sum_{i=1}^N \ln(k_i !) - N\ln(\Gamma(r)) + \sum_{i=1}^N k_i \ln(1-p) + Nr \ln(p).$$

To find the maximum we take the partial derivatives with respect to r and p and set them equal to zero:

 * $$\frac{\partial \ell(r,p)}{\partial p} = -\left[\sum_{i=1}^N k_i \frac{1}{1-p}\right] + Nr \frac{1}{p} = 0$$ and

 * $$\frac{\partial \ell(r,p)}{\partial r} = \left[\sum_{i=1}^N \psi(k_i + r)\right] - N\psi(r) + N\ln(p) = 0$$

where

 * $$\psi(k) = \frac{\Gamma'(k)}{\Gamma(k)} \!$$ is the digamma function.

Solving the first equation for p gives:

 * $$p = \frac{Nr} {Nr + \sum_{i=1}^N k_i}$$

Substituting this in the second equation gives:

 * $$\frac{\partial \ell(r,p)}{\partial r} = \left[\sum_{i=1}^N \psi(k_i + r)\right] - N\psi(r) + N\ln\left(\frac{r}{r + \sum_{i=1}^N k_i/N}\right) = 0$$

This equation cannot be solved for r in closed form. If a numerical solution is desired, an iterative technique such as Newton's method can be used. Alternatively, the expectation–maximization algorithm can be used.

Waiting time in a Bernoulli process
For the special case where r is an integer, the negative binomial distribution is known as the Pascal distribution. It is the probability distribution of a certain number of failures and successes in a series of independent and identically distributed Bernoulli trials. For k + r Bernoulli trials with success probability p, the negative binomial gives the probability of k successes and r failures, with a failure on the last trial. In other words, the negative binomial distribution is the probability distribution of the number of successes before the rth failure in a Bernoulli process, with probability p of successes on each trial. A Bernoulli process is a discrete time process, and so the number of trials, failures, and successes are integers.

Consider the following example. Suppose we repeatedly throw a die, and consider a 1 to be a failure. The probability of success on each trial is 5/6. The number of successes before the third failure belongs to the infinite set { 0, 1, 2, 3, ... }. That number of successes is a negative-binomially distributed random variable.

When r = 1 we get the probability distribution of number of successes before the first failure (i.e. the probability of the first failure occurring on the (k + 1)st trial), which is a geometric distribution:

f(k; r, p) = (1-p) \cdot p^k \! $$

Recent findings suggest that the waiting time in a Bernoulli process is strongly related to fractals and Dirichlet function. Probability distributions with fractal properties that are related to Dirichlet function can be derived from recurrent processes generated by uniform discrete distributions. Such uniform discrete distributions can be pi digits, flips of a fair dice or live casino spins. Consider the following waiting time in a Bernoulli process: A random variable C$i$ is repeatedly sampled N times from a discrete uniform distribution, where i ranges from 1 to N. For instance, consider integer values ranging from 1 to 10. Moments of occurrence, T$k$, signify when events C$i$ repeat, defined as C$i$ = C$i-1$ or C$i$ = C$i-2$, where k ranges from 1 to M, with M being less than N. Subsequently, define S$j$ as the interval between successive T$k$, representing the waiting time for an event to occur. Finally, introduce Z$l$ as ln(S$j$) – ln(S$j-1$), where l ranges from 1 to U-1. The random variable Z displays fractal properties, resembling the shape distribution akin to Thomae's or Dirichlet function.

Overdispersed Poisson
The negative binomial distribution, especially in its alternative parameterization described above, can be used as an alternative to the Poisson distribution. It is especially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such cases, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. Hence a Poisson distribution is not an appropriate model. Since the negative binomial distribution has one more parameter than the Poisson, the second parameter can be used to adjust the variance independently of the mean. See Cumulants of some discrete probability distributions.

An application of this is to annual counts of tropical cyclones in the North Atlantic or to monthly to 6-monthly counts of wintertime extratropical cyclones over Europe, for which the variance is greater than the mean. In the case of modest overdispersion, this may produce substantially similar results to an overdispersed Poisson distribution.

Negative binomial modeling is widely employed in ecology and biodiversity research for analyzing count data where overdispersion is very common. This is because overdispersion is indicative of biological aggregation, such as species or communities forming clusters. Ignoring overdispersion can lead to significantly inflated model parameters, resulting in misleading statistical inferences. The negative binomial distribution effectively addresses overdispersed counts by permitting the variance to vary quadratically with the mean. An additional dispersion parameter governs the slope of the quadratic term, determining the severity of overdispersion. The model's quadratic mean-variance relationship proves to be a realistic approach for handling overdispersion, as supported by empirical evidence from many studies. Overall, the NB model offers two attractive features: (1) the convenient interpretation of the dispersion parameter as an index of clustering or aggregation, and (2) its tractable form, featuring a closed expression for the probability mass function.

In genetics, the negative binomial distribution is commonly used to model data in the form of discrete sequence read counts from high-throughput RNA and DNA sequencing experiments.

In epidemiology of infectious diseases, the negative binomial has been used as a better option than the Poisson distribution to model overdispersed counts of secondary infections from one infected case (super-spreading events).

Multiplicity observations (physics)
The negative binomial distribution has been the most effective statistical model for a broad range of multiplicity observations in particle collision experiments, e.g., $$p\bar p,\ hh,\ hA,\ AA,\ e^{+}e^-$$    (See for an overview), and is argued to be a scale-invariant property of matter,  providing the best fit for astronomical observations, where it predicts the number of galaxies in a region of space. The phenomenological justification for the effectiveness of the negative binomial distribution in these contexts remained unknown for fifty years, since their first observation in 1973. In 2023, a proof from first principles was eventually demonstrated by Scott V. Tezlaf, where it was shown that the negative binomial distribution emerges from symmetries in the dynamical equations of a canonical ensemble of particles in Minkowski space. Roughly, given an expected number of trials $$\langle n \rangle$$ and expected number of successes $$\langle r \rangle$$, where

 * $$\langle \mathcal{n} \rangle - \langle r \rangle = k, \quad \quad  \langle p \rangle  = \frac{\langle r \rangle}{\langle \mathcal{n} \rangle}  \quad\quad \quad \implies \quad\quad \quad

\langle \mathcal{n} \rangle = \frac{k}{1-\langle p \rangle}, \quad \quad \langle {r} \rangle = \frac{k\langle p \rangle}{1 - \langle p \rangle},$$

an isomorphic set of equations can be identified with the parameters of a relativistic current density of a canonical ensemble of massive particles, via

 * $$c^2\langle \rho^2 \rangle - \langle j^2 \rangle = c^2\rho_0^2, \quad \quad  \quad \langle \beta^2_v \rangle = \frac{\langle j^2 \rangle}{c^2\langle \rho^2 \rangle}  \quad \quad \implies \quad \quad

c^2\langle \rho^2 \rangle = \frac{c^2\rho_0^2}{1-\langle \beta^2_v \rangle}, \quad \quad  \quad \langle j^2 \rangle = \frac{c^2\rho_0^2  \langle \beta^2_v \rangle}{1-\langle \beta^2_v \rangle},$$

where $$\rho_0$$ is the rest density, $$\langle \rho ^2 \rangle$$ is the relativistic mean square density, $$\langle j ^2 \rangle$$ is the relativistic mean square current density, and $$\langle \beta^2_v \rangle=\langle v^2 \rangle /c^2$$, where $$\langle v ^2 \rangle$$ is the mean square speed of the particle ensemble and $$c$$ is the speed of light—such that one can establish the following bijective map:

 * $$c^2\rho_0^2 \mapsto k, \quad \quad \langle \beta^2_v \rangle \mapsto \langle p \rangle, \quad \quad c^2\langle\rho^2 \rangle \mapsto \langle \mathcal{n} \rangle, \quad \quad \langle j^2 \rangle \mapsto \langle r \rangle.$$

A rigorous alternative proof of the above correspondence has also been demonstrated through quantum mechanics via the Feynman path integral.

History
This distribution was first studied in 1713 by Pierre Remond de Montmort in his Essay d'analyse sur les jeux de hazard, as the distribution of the number of trials required in an experiment to obtain a given number of successes. It had previously been mentioned by Pascal.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Negative binomial distribution


text:
Process (computing)

In computing, a process is the instance of a computer program that is being executed by one or many threads. There are many different process models, some of which are light weight, but almost all processes (even entire virtual machines) are rooted in an operating system (OS) process which comprises the program code, assigned system resources, physical and logical access permissions, and data structures to initiate, control and coordinate execution activity. Depending on the OS, a process may be made up of multiple threads of execution that execute instructions concurrently.

While a computer program is a passive collection of instructions typically stored in a file on disk, a process is the execution of those instructions after being loaded from the disk into memory. Several processes may be associated with the same program; for example, opening up several instances of the same program often results in more than one process being executed.

Multitasking is a method to allow multiple processes to share processors (CPUs) and other system resources. Each CPU (core) executes a single process at a time. However, multitasking allows each processor to switch between tasks that are being executed without having to wait for each task to finish (preemption). Depending on the operating system implementation, switches could be performed when tasks initiate and wait for completion of input/output operations, when a task voluntarily yields the CPU, on hardware interrupts, and when the operating system scheduler decides that a process has expired its fair share of CPU time (e.g, by the Completely Fair Scheduler of the Linux kernel).

A common form of multitasking is provided by CPU's time-sharing that is a method for interleaving the execution of users' processes and threads, and even of independent kernel tasks – although the latter feature is feasible only in preemptive kernels such as Linux. Preemption has an important side effect for interactive processes that are given higher priority with respect to CPU bound processes, therefore users are immediately assigned computing resources at the simple pressing of a key or when moving a mouse. Furthermore, applications like video and music reproduction are given some kind of real-time priority, preempting any other lower priority process. In time-sharing systems, context switches are performed rapidly, which makes it seem like multiple processes are being executed simultaneously on the same processor. This seemingly-simultaneous execution of multiple processes is called concurrency.

For security and reliability, most modern operating systems prevent direct communication between independent processes, providing strictly mediated and controlled inter-process communication.

Representation
In general, a computer system process consists of (or is said to own) the following resources:
 * An image of the executable machine code associated with a program.
 * Memory (typically some region of virtual memory); which includes the executable code, process-specific data (input and output), a call stack (to keep track of active subroutines and/or other events), and a heap to hold intermediate computation data generated during run time.
 * Operating system descriptors of resources that are allocated to the process, such as file descriptors (Unix terminology) or handles (Windows), and data sources and sinks.
 * Security attributes, such as the process owner and the process' set of permissions (allowable operations).
 * Processor state (context), such as the content of registers and physical memory addressing. The state is typically stored in computer registers when the process is executing, and in memory otherwise.

The operating system holds most of this information about active processes in data structures called process control blocks. Any subset of the resources, typically at least the processor state, may be associated with each of the process' threads in operating systems that support threads or child processes.

The operating system keeps its processes separate and allocates the resources they need, so that they are less likely to interfere with each other and cause system failures (e.g., deadlock or thrashing). The operating system may also provide mechanisms for inter-process communication to enable processes to interact in safe and predictable ways.

Multitasking and process management
A multitasking operating system may just switch between processes to give the appearance of many processes executing simultaneously (that is, in parallel), though in fact only one process can be executing at any one time on a single CPU (unless the CPU has multiple cores, then multithreading or other similar technologies can be used).

It is usual to associate a single process with a main program, and child processes with any spin-off, parallel processes, which behave like asynchronous subroutines. A process is said to own resources, of which an image of its program (in memory) is one such resource. However, in multiprocessing systems many processes may run off of, or share, the same reentrant program at the same location in memory, but each process is said to own its own image of the program.

Processes are often called "tasks" in embedded operating systems. The sense of "process" (or task) is "something that takes up time", as opposed to "memory", which is "something that takes up space".

The above description applies to both processes managed by an operating system, and processes as defined by process calculi.

If a process requests something for which it must wait, it will be blocked. When the process is in the blocked state, it is eligible for swapping to disk, but this is transparent in a virtual memory system, where regions of a process's memory may be really on disk and not in main memory at any time. Even portions of active processes/tasks (executing programs) are eligible for swapping to disk, if the portions have not been used recently. Not all parts of an executing program and its data have to be in physical memory for the associated process to be active.

Process states

An operating system kernel that allows multitasking needs processes to have certain states. Names for these states are not standardised, but they have similar functionality.

 * First, the process is "created" by being loaded from a secondary storage device (hard disk drive, CD-ROM, etc.) into main memory. After that the process scheduler assigns it the "waiting" state.
 * While the process is "waiting", it waits for the scheduler to do a so-called context switch. The context switch loads the process into the processor and changes the state to "running" while the previously "running" process is stored in a "waiting" state.
 * If a process in the "running" state needs to wait for a resource (wait for user input or file to open, for example), it is assigned the "blocked" state. The process state is changed back to "waiting" when the process no longer needs to wait (in a blocked state).
 * Once the process finishes execution, or is terminated by the operating system, it is no longer needed. The process is removed instantly or is moved to the "terminated" state. When removed, it just waits to be removed from main memory.

Inter-process communication
When processes need to communicate with each other they must share parts of their address spaces or use other forms of inter-process communication (IPC). For instance in a shell pipeline, the output of the first process needs to pass to the second one, and so on. Another example is a task that has been decomposed into cooperating but partially independent processes which can run simultaneously (i.e., using concurrency, or true parallelism – the latter model is a particular case of concurrent execution and is feasible whenever multiple CPU cores are available for the processes that are ready to run).

It is even possible for two or more processes to be running on different machines that may run different operating system (OS), therefore some mechanisms for communication and synchronization (called communications protocols for distributed computing) are needed (e.g., the Message Passing Interface {MPI}).

History
By the early 1960s, computer control software had evolved from monitor control software, for example IBSYS, to executive control software. Over time, computers got faster while computer time was still neither cheap nor fully utilized; such an environment made multiprogramming possible and necessary. Multiprogramming means that several programs run concurrently. At first, more than one program ran on a single processor, as a result of underlying uniprocessor computer architecture, and they shared scarce and limited hardware resources; consequently, the concurrency was of a serial nature. On later systems with multiple processors, multiple programs may run concurrently in parallel.

Programs consist of sequences of instructions for processors. A single processor can run only one instruction at a time: it is impossible to run more programs at the same time. A program might need some resource, such as an input device, which has a large delay, or a program might start some slow operation, such as sending output to a printer. This would lead to processor being "idle" (unused). To keep the processor busy at all times, the execution of such a program is halted and the operating system switches the processor to run another program. To the user, it will appear that the programs run at the same time (hence the term "parallel").

Shortly thereafter, the notion of a "program" was expanded to the notion of an "executing program and its context". The concept of a process was born, which also became necessary with the invention of re-entrant code. Threads came somewhat later. However, with the advent of concepts such as time-sharing, computer networks, and multiple-CPU shared memory computers, the old "multiprogramming" gave way to true multitasking, multiprocessing and, later, multithreading.

title: Process (computing)