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On the negative binomial distribution and its generalizations

Author

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  • Vellaisamy, P.
  • Upadhye, N.S.

Abstract

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.

Suggested Citation

  • Vellaisamy, P. & Upadhye, N.S., 2007. "On the negative binomial distribution and its generalizations," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 173-180, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:2:p:173-180
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    References listed on IDEAS

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    1. Shishebor, Z. & Towhidi, M., 2004. "On the generalization of negative binomial distribution," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 127-133, January.
    2. P. Vellaisamy & S. Sankar, 2005. "A Unified Approach for Modeling and Designing Attribute Sampling Plans for Monitoring Dependent Production Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 307-323, September.
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    Cited by:

    1. Sónia Gouveia & Manuel G. Scotto & Christian H. Weiß & Paulo Jorge S. G. Ferreira, 2017. "Binary auto-regressive geometric modelling in a DNA context," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 253-271, February.

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