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

• 作者: Estela M. P. Bereta Francisco Louzada Maria A. P. Franco
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: COMPOUNDING DISTRIBUTIONS DISTRIBUTION of the MAXIMUM DISTRIBUTION of the Minimum Probability Generating Function
• 年，卷（期）: 2012,（4）
• 页码范围: 350-353
• 页数: 4页
• 分类号: O1

摘要

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).