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Characterizations using the generalized reversed lack of memory property

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  • Asha, G.
  • Rejeesh, C. John

Abstract

A binary operator * over real numbers is said to be associative if (x*y)*z=x*(y*z) and is said to be reducible if x*y=x*z if and only if y=z and if y*w=z*w if and only if y=z. The operation is said to have an identity element e if x*e=x. In this paper a characterization of a subclass of the reversed generalized Pareto distribution [Castillo, E. Hadi, A.S., 1995. Modelling life time data with applications to fatigue models. Journal of American Statistical Association. 90 (431), 1041-1054] is generalized using this operator. The idea is extended to the bivariate case too and it is shown that it characterizes a class of bivariate distributions containing the characterized extension (CE) model of Roy [Roy, D. 2002a. A characterization of model approach for generating bivariate life distributions using reversed hazard rates. Journal of Japan Statistical Society 32 (2), 239-245].

Suggested Citation

  • Asha, G. & Rejeesh, C. John, 2009. "Characterizations using the generalized reversed lack of memory property," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1480-1487, June.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:12:p:1480-1487
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    References listed on IDEAS

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    1. Asok Nanda & Moshe Shaked, 2001. "The Hazard Rate and the Reversed Hazard Rate Orders, with Applications to Order Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 853-864, December.
    2. Dilip Roy, 2002. "On Bivariate Lack of Memory Property and a New Definition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 404-410, June.
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    Cited by:

    1. G. Asha & C. Rejeesh, 2015. "Characterizations using past entropy measures," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 119-134, April.
    2. Mervat Mahdy, 2014. "Further results involving percentile inactivity time order and its inference," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 269-282, October.

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