Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\)
We study the distributions of waiting times in variations of the negative binomial distribution of order \(k\). One variation apply different enumeration scheme on the runs of successes. Another case considers binary trials for which the probability of ones is geometrically varying. We investigate t...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2024-03 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Oh, Jungtaek |
| description | We study the distributions of waiting times in variations of the negative binomial distribution of order \(k\). One variation apply different enumeration scheme on the runs of successes. Another case considers binary trials for which the probability of ones is geometrically varying. We investigate the exact distribution of the waiting time for the \(r\)-th occurrence of success run of a specified length (non-overlapping, overlapping, at least, exactly, \(\ell\)-overlapping) in a \(q\)-sequence of binary trials. The main theorems are Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\) and \(q\)-negative binomial distribution of order \(k\) in the \(\ell\)-overlapping case. In the present work, we consider a sequence of independent binary zero and one trials with not necessarily identical distribution with the probability of ones varying according to a geometric rule. Exact formulae for the distributions obtained by means of enumerative combinatorics. |
| format | Article |
| fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2723273823</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2723273823</sourcerecordid><originalsourceid>FETCH-proquest_journals_27232738233</originalsourceid><addsrcrecordid>eNqNjtEKgjAYRkcQJOU7DLpxkKD_NL2PogeQrgYy2YyZbbrNoLdvUA_Q1TnwnYtvhSKgNE_rAmCDYueGLMvgWEFZ0gjdmvckMUtyRg4B8AVlBHMtghXBWDIzkmp55169JO6UNk_FRyyU81Z1i1dGY9NjY4W0oX4wskPrno9Oxj9u0f5ybk7XdLJmXqTz7WAWq8PUQgUUKlqHk_9VHzYsPG4</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2723273823</pqid></control><display><type>article</type><title>Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\)</title><source>Free E- Journals</source><creator>Oh, Jungtaek</creator><creatorcontrib>Oh, Jungtaek</creatorcontrib><description>We study the distributions of waiting times in variations of the negative binomial distribution of order \(k\). One variation apply different enumeration scheme on the runs of successes. Another case considers binary trials for which the probability of ones is geometrically varying. We investigate the exact distribution of the waiting time for the \(r\)-th occurrence of success run of a specified length (non-overlapping, overlapping, at least, exactly, \(\ell\)-overlapping) in a \(q\)-sequence of binary trials. The main theorems are Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\) and \(q\)-negative binomial distribution of order \(k\) in the \(\ell\)-overlapping case. In the present work, we consider a sequence of independent binary zero and one trials with not necessarily identical distribution with the probability of ones varying according to a geometric rule. Exact formulae for the distributions obtained by means of enumerative combinatorics.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Combinatorial analysis ; Enumeration</subject><ispartof>arXiv.org, 2024-03</ispartof><rights>2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>777,781</link.rule.ids></links><search><creatorcontrib>Oh, Jungtaek</creatorcontrib><title>Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\)</title><title>arXiv.org</title><description>We study the distributions of waiting times in variations of the negative binomial distribution of order \(k\). One variation apply different enumeration scheme on the runs of successes. Another case considers binary trials for which the probability of ones is geometrically varying. We investigate the exact distribution of the waiting time for the \(r\)-th occurrence of success run of a specified length (non-overlapping, overlapping, at least, exactly, \(\ell\)-overlapping) in a \(q\)-sequence of binary trials. The main theorems are Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\) and \(q\)-negative binomial distribution of order \(k\) in the \(\ell\)-overlapping case. In the present work, we consider a sequence of independent binary zero and one trials with not necessarily identical distribution with the probability of ones varying according to a geometric rule. Exact formulae for the distributions obtained by means of enumerative combinatorics.</description><subject>Combinatorial analysis</subject><subject>Enumeration</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNjtEKgjAYRkcQJOU7DLpxkKD_NL2PogeQrgYy2YyZbbrNoLdvUA_Q1TnwnYtvhSKgNE_rAmCDYueGLMvgWEFZ0gjdmvckMUtyRg4B8AVlBHMtghXBWDIzkmp55169JO6UNk_FRyyU81Z1i1dGY9NjY4W0oX4wskPrno9Oxj9u0f5ybk7XdLJmXqTz7WAWq8PUQgUUKlqHk_9VHzYsPG4</recordid><startdate>20240318</startdate><enddate>20240318</enddate><creator>Oh, Jungtaek</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240318</creationdate><title>Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\)</title><author>Oh, Jungtaek</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_27232738233</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Combinatorial analysis</topic><topic>Enumeration</topic><toplevel>online_resources</toplevel><creatorcontrib>Oh, Jungtaek</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Oh, Jungtaek</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\)</atitle><jtitle>arXiv.org</jtitle><date>2024-03-18</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>We study the distributions of waiting times in variations of the negative binomial distribution of order \(k\). One variation apply different enumeration scheme on the runs of successes. Another case considers binary trials for which the probability of ones is geometrically varying. We investigate the exact distribution of the waiting time for the \(r\)-th occurrence of success run of a specified length (non-overlapping, overlapping, at least, exactly, \(\ell\)-overlapping) in a \(q\)-sequence of binary trials. The main theorems are Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\) and \(q\)-negative binomial distribution of order \(k\) in the \(\ell\)-overlapping case. In the present work, we consider a sequence of independent binary zero and one trials with not necessarily identical distribution with the probability of ones varying according to a geometric rule. Exact formulae for the distributions obtained by means of enumerative combinatorics.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2024-03 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_proquest_journals_2723273823 |
| source | Free E- Journals |
| subjects | Combinatorial analysis Enumeration |
| title | Type \(1\), \(2\), \(3\) and \(4\) \(q\)-negative binomial distribution of order \(k\) |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-19T02%3A46%3A11IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Type%20%5C(1%5C),%20%5C(2%5C),%20%5C(3%5C)%20and%20%5C(4%5C)%20%5C(q%5C)-negative%20binomial%20distribution%20of%20order%20%5C(k%5C)&rft.jtitle=arXiv.org&rft.au=Oh,%20Jungtaek&rft.date=2024-03-18&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2723273823%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2723273823&rft_id=info:pmid/&rfr_iscdi=true |