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Characterization of distributions through failure rate and mean residual life functions

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  • Nanda, Asok K.

Abstract

Makino [Makino, T., 1984. Mean hazard rate and its applications to the normal approximation of the Weibull distribution. Naval Research Logistics Quarterly 31, 1-8] proves that, for any random variable X with finite mean [mu], E(1/r(X)][greater-or-equal, slanted]1/[mu], where r([dot operator]) is the failure rate function of X, with equality if and only if X is exponentially distributed. Here we characterize exponential distribution and Rayleigh distribution through the expected values of r(X) and e(X), where e([dot operator]) is the mean residual life function of X.

Suggested Citation

  • Nanda, Asok K., 2010. "Characterization of distributions through failure rate and mean residual life functions," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 752-755, May.
  • Handle: RePEc:eee:stapro:v:80:y:2010:i:9-10:p:752-755
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    Cited by:

    1. Farouk Metiri & Halim Zeghdoudi & Abdelali Ezzebsa, 2022. "On the characterisation of X-Lindley distribution by truncated moments. Properties and application," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 97-109.
    2. Wang, Shaochen & Weiß, Christian H., 2023. "New characterizations of the (discrete) Lindley distribution and their applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 310-322.
    3. Szymkowiak, Magdalena & Iwińska, Maria, 2016. "Characterizations of Discrete Weibull related distributions," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 41-48.
    4. Bhattacharjee, Subarna & Nanda, Asok K. & Misra, Satya Kr., 2013. "Inequalities involving expectations to characterize distributions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2113-2118.

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