On the negative binomial distribution and its generalizations
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- 作者：P. Vellaisamy ; N.S. Upadhye
- 关键词：Sums of random variables ; Characterizations ; Binomial moments ; Geometric distribution ; Negative binomial distribution ; Bernoulli sequences ; Probabilistic models ; Generalized negative binomial distributions
- 刊名：Statistics and Probability Letters
- 出版年：2007
- 出版时间：15 January 2007
- 年：2007
- 卷：77
- 期：2
- 页码：173-180
- 全文大小：163 K
文摘
It is shown that the negative binomial distribution NB(r,p) may arise out of an identical but dependent geometric sequence. Using a general characterization result for NB(r,p), based on a non-negative integer -valued sequence, we show that NB(2,p) may arise as the distribution of the sum of -valued random variables which are neither geometric nor independent. We show also that NB(r,p) arises, as the distribution of the number of trials for the rth success, based on a sequence of dependent Bernoulli variables. The generalized negative binomial distributions arising out of certain dependent Bernoulli sequences are also investigated. In particular, certain erroneous results in the literature are corrected.