On the Distribution of the Minimum or Maximum of a Random Number of i.i.d. Lifetime Random Variables

Francisco Louzada; Estela MPBereta; Maria APFranco

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On the Distribution of the Minimum or Maximum of a Random Number of i.i.d. Lifetime Random Variables

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Statisticians are usually concerned with the proposition of new distributions. In this paper we point out that a unified and concise derivation procedure of the distribution of the minimum or maximum of a random number N of indepen-dent and identically distributed continuous random variables Yi,{i = 1,2,…,N} is obtained if one compounds the probability generating function of N with the survival or the distribution func-tion of Yi. Expressions are then derived in closed form for the density, hazard and quantile func-tions of the minimum or maximum. The methodology is illustrated with examples of the distributions proposed by Adamidis and Loukas (1998), Kus (2007), Tahmasbi and Rezaei (2008), Barreto-Souza and Cribari-Neto (2009), Cancho, Louzada, and Barriga (2011) and Louzada, Roman and Cancho (2011).

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来源
《应用数学（英文）》 |2012年第4期|350-353|共4页
作者
Francisco Louzada; Estela MPBereta; Maria APFranco;
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作者单位

Department of Applied Mathematics&Statistics;

ICMC;

Universidade de Sao Paulo;

Sao Paulo;

Brazil;

Department of Statistics;

CCET;

Universidade Federal de Sao Carlos;

Sao Carlos;

Brazil;

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原文格式 PDF
正文语种 chi
中图分类数学;
关键词
Compounding Distributions; Distribution of the Maximum; Distribution of the Minimum; Probability Generating Function;

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On the Distribution of the Minimum or Maximum of a Random Number of i.i.d. Lifetime Random Variables

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