Distribution Theory of Runs: A Markov Chain Approach
The statistics of the number of success runs in a sequence of Bernoulli trials have been used in many statistical areas. For almost a century, even in the simplest case of independent and identically distributed Bernoulli trials, the exact distributions of many run statistics still remain unknown. D...
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| Veröffentlicht in: | Journal of the American Statistical Association 1994-09, Vol.89 (427), p.1050-1058 |
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| container_title | Journal of the American Statistical Association |
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| creator | Fu, J. C. Koutras, M. V. |
| description | The statistics of the number of success runs in a sequence of Bernoulli trials have been used in many statistical areas. For almost a century, even in the simplest case of independent and identically distributed Bernoulli trials, the exact distributions of many run statistics still remain unknown. Departing from the traditional combinatorial approach, in this article we present a simple unified approach for the distribution theory of runs based on a finite Markov chain imbedding technique. Our results cover not only the identical Bernoulli trials, but also the nonidentical Bernoulli trials. As a byproduct, our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run. |
| doi_str_mv | 10.1080/01621459.1994.10476841 |
| format | Article |
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C. ; Koutras, M. V.</creator><creatorcontrib>Fu, J. C. ; Koutras, M. V.</creatorcontrib><description>The statistics of the number of success runs in a sequence of Bernoulli trials have been used in many statistical areas. For almost a century, even in the simplest case of independent and identically distributed Bernoulli trials, the exact distributions of many run statistics still remain unknown. Departing from the traditional combinatorial approach, in this article we present a simple unified approach for the distribution theory of runs based on a finite Markov chain imbedding technique. Our results cover not only the identical Bernoulli trials, but also the nonidentical Bernoulli trials. As a byproduct, our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run.</description><identifier>ISSN: 0162-1459</identifier><identifier>EISSN: 1537-274X</identifier><identifier>DOI: 10.1080/01621459.1994.10476841</identifier><identifier>CODEN: JSTNAL</identifier><language>eng</language><publisher>Alexandria, VA: Taylor & Francis Group</publisher><subject>Bernoulli Hypothesis ; Bernoulli random variables ; Binomial distributions ; Distribution theory ; Exact sciences and technology ; Markov analysis ; Markov chains ; Mathematical moments ; Mathematics ; Matrices ; Patterns ; Probabilities ; Probability and statistics ; Quality assurance ; Random variables ; Reliability ; Sciences and techniques of general use ; Statistical theories ; Statistics ; Theory and Methods ; Transition probabilities ; Transition probability matrix</subject><ispartof>Journal of the American Statistical Association, 1994-09, Vol.89 (427), p.1050-1058</ispartof><rights>Copyright Taylor & Francis Group, LLC 1994</rights><rights>Copyright 1994 American Statistical Association</rights><rights>1995 INIST-CNRS</rights><rights>Copyright American Statistical Association Sep 1994</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c379t-b7150cb09612d5266928c2c81291d9ca039b0f4216f104eba2a5e96c9ec632cc3</citedby><cites>FETCH-LOGICAL-c379t-b7150cb09612d5266928c2c81291d9ca039b0f4216f104eba2a5e96c9ec632cc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2290933$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2290933$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27924,27925,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3317371$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Fu, J. C.</creatorcontrib><creatorcontrib>Koutras, M. V.</creatorcontrib><title>Distribution Theory of Runs: A Markov Chain Approach</title><title>Journal of the American Statistical Association</title><description>The statistics of the number of success runs in a sequence of Bernoulli trials have been used in many statistical areas. For almost a century, even in the simplest case of independent and identically distributed Bernoulli trials, the exact distributions of many run statistics still remain unknown. Departing from the traditional combinatorial approach, in this article we present a simple unified approach for the distribution theory of runs based on a finite Markov chain imbedding technique. Our results cover not only the identical Bernoulli trials, but also the nonidentical Bernoulli trials. As a byproduct, our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run.</description><subject>Bernoulli Hypothesis</subject><subject>Bernoulli random variables</subject><subject>Binomial distributions</subject><subject>Distribution theory</subject><subject>Exact sciences and technology</subject><subject>Markov analysis</subject><subject>Markov chains</subject><subject>Mathematical moments</subject><subject>Mathematics</subject><subject>Matrices</subject><subject>Patterns</subject><subject>Probabilities</subject><subject>Probability and statistics</subject><subject>Quality assurance</subject><subject>Random variables</subject><subject>Reliability</subject><subject>Sciences and techniques of general use</subject><subject>Statistical theories</subject><subject>Statistics</subject><subject>Theory and Methods</subject><subject>Transition probabilities</subject><subject>Transition probability matrix</subject><issn>0162-1459</issn><issn>1537-274X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1994</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNqFkF9LwzAUxYMoOKdfQYr42pmbtEnjW5l_YSLIBN9CmrUss2tm0ir99qZsk715Xy5cfvfccw9Cl4AngDN8g4ERSFIxASGSMEo4yxI4QiNIKY8JTz6O0WiA4oE6RWfer3AonmUjlNwZ3zpTdK2xTTRfltb1ka2it67xt1EevSj3ab-j6VKZJso3G2eVXp6jk0rVvrzY9TF6f7ifT5_i2evj8zSfxZpy0cYFhxTrAgsGZJESxgTJNNEZEAELoRWmosBVQoBVwXVZKKLSUjAtSs0o0ZqO0dVWN5z96krfypXtXBNOyvBWxnGaQoDYFtLOeu_KSm6cWSvXS8ByCEjuA5JDQHIfUFi83qkrr1VdOdVo4_-2KQVO-QG28q11h-KEYi4JEVhQGrB8i5mmsm6tfqyrF7JVfW3dXpr-4-gXKEOChQ</recordid><startdate>19940901</startdate><enddate>19940901</enddate><creator>Fu, J. 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C. ; Koutras, M. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c379t-b7150cb09612d5266928c2c81291d9ca039b0f4216f104eba2a5e96c9ec632cc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1994</creationdate><topic>Bernoulli Hypothesis</topic><topic>Bernoulli random variables</topic><topic>Binomial distributions</topic><topic>Distribution theory</topic><topic>Exact sciences and technology</topic><topic>Markov analysis</topic><topic>Markov chains</topic><topic>Mathematical moments</topic><topic>Mathematics</topic><topic>Matrices</topic><topic>Patterns</topic><topic>Probabilities</topic><topic>Probability and statistics</topic><topic>Quality assurance</topic><topic>Random variables</topic><topic>Reliability</topic><topic>Sciences and techniques of general use</topic><topic>Statistical theories</topic><topic>Statistics</topic><topic>Theory and Methods</topic><topic>Transition probabilities</topic><topic>Transition probability matrix</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fu, J. 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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Bernoulli Hypothesis Bernoulli random variables Binomial distributions Distribution theory Exact sciences and technology Markov analysis Markov chains Mathematical moments Mathematics Matrices Patterns Probabilities Probability and statistics Quality assurance Random variables Reliability Sciences and techniques of general use Statistical theories Statistics Theory and Methods Transition probabilities Transition probability matrix |
| title | Distribution Theory of Runs: A Markov Chain Approach |
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