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On relative log-concavity and stochastic comparisons

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  • Fang, Rui
  • Ding, Weiyong

Abstract

In this paper, we investigate the equivalence among stochastic orderings between random variables under the scenario where the ratio of density functions or survival functions is log-concave. Some sufficient and necessary conditions that may be easily checked for the usual stochastic order, the hazard rate order, the mean residual lifetime order, the harmonic mean residual lifetime order and the mean inactivity time order are presented. As for illustration, we also provide several numerical examples and three applications.

Suggested Citation

  • Fang, Rui & Ding, Weiyong, 2018. "On relative log-concavity and stochastic comparisons," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 91-98.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:91-98
    DOI: 10.1016/j.spl.2018.01.007
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    References listed on IDEAS

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    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. 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.
    3. Kochar, Subhash C & Korwar, Ramesh, 1996. "Stochastic Orders for Spacings of Heterogeneous Exponential Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 69-83, April.
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