2009•Unpublished venueRequires access

Some Representations and Specifications of the Generalized Negative Binomial Distribution

Mina Towhidi

Abstract

Abstract: In a sequence of dependent Bernoulli trials, the distribution of the number of trials required to obtain r successes, Vr, is called a Generalized Negative Binomial (GNB) distribution. We present a simple representation of this distribution based on moments and consider the conditions under which a GNB distribution follows negative binomial distribution. Also we study the properties of this distribution in Markov chains. Key words: Negative binomial distribution • Dependent Bernoulli sequences • Generalized negative

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Key concepts: Beta-binomial distribution, Beta negative binomial distribution, Mathematics, Binomial distribution, Negative binomial distribution, Multinomial distribution, Negative multinomial distribution, Bernoulli trial