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Stochastic comparisons of Poisson and binomial random variables with their mixtures

Author

Listed:
  • Misra, Neeraj
  • Singh, Harshinder
  • James Harner, E.

Abstract

Motivated by an ecological sampling problem, we compare a Poisson distribution having a fixed mean with a Poisson distribution having a random mean, which has an arbitrary continuous (or discrete) probability distribution. These comparisons are made with respect to the likelihood ratio ordering, simple stochastic ordering, uniform variability ordering and expectation ordering. As a particular case, the mixed Poisson and the Poisson distribution with a fixed mean are compared when both the distributions have the same mean. Similar comparisons are made between the mixed binomial and the binomial distribution having a fixed probability of success.

Suggested Citation

  • Misra, Neeraj & Singh, Harshinder & James Harner, E., 2003. "Stochastic comparisons of Poisson and binomial random variables with their mixtures," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 279-290, December.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:279-290
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    References listed on IDEAS

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    1. Harshinder Singh, 1989. "On partial orderings of life distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 103-110, February.
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    Cited by:

    1. Alamatsaz, Mohammad Hossein & Abbasi, Somayyeh, 2008. "Ordering comparison of negative binomial random variables with their mixtures," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2234-2239, October.
    2. Fang, Rui & Ding, Weiyong, 2018. "On relative log-concavity and stochastic comparisons," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 91-98.

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