[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/negative-binomial-distribution-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/negative-binomial-distribution-wikipedia\/","headline":"Negative binomial distribution – Wikipedia","name":"Negative binomial distribution – Wikipedia","description":"before-content-x4 Probability distribution after-content-x4 Probability mass function The orange line represents the mean, which is equal to 10 in each","datePublished":"2014-02-04","dateModified":"2014-02-04","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/8\/83\/Negbinomial.gif","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/8\/83\/Negbinomial.gif","height":"149","width":"250"},"url":"https:\/\/wiki.edu.vn\/en\/negative-binomial-distribution-wikipedia\/","wordCount":34791,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4Probability distribution       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Probability mass functionThe orange line represents the mean, which is equal to 10 in each of these plots; the green line shows the standard deviation.NotationNB(r,p){displaystyle mathrm {NB} (r,,p)}Parametersr > 0 \u2014 number of successes until the experiment is stopped (integer, but the definition can also be extended to reals)p \u2208 [0,1] \u2014 success probability in each experiment (real)Supportk \u2208 {\u20090, 1, 2, 3, \u2026\u2009} \u2014 number of failuresPMF       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4k\u21a6(k+r\u22121k)\u22c5(1\u2212p)kpr,{displaystyle kmapsto {k+r-1 choose k}cdot (1-p)^{k}p^{r},} involving a binomial coefficientCDFk\u21a61\u2212Ip(k+1,r),{displaystyle kmapsto 1-I_{p}(k+1,,r),} the regularized incomplete beta functionMeanr(1\u2212p)p{displaystyle {frac {r(1-p)}{p}}}Mode"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/negative-binomial-distribution-wikipedia\/#breadcrumbitem","name":"Negative binomial distribution – Wikipedia"}}]}]