On the Distribution of the Minimum or Maximum of a Random Number of i.i.d. Lifetime Random VariablesReport as inadecuate




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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.

KEYWORDS

Compounding Distributions; Distribution of the Maximum; Distribution of the Minimum; Probability Generating Function

Cite this paper

F. Louzada, E. Bereta and M. Franco -On the Distribution of the Minimum or Maximum of a Random Number of i.i.d. Lifetime Random Variables,- Applied Mathematics, Vol. 3 No. 4, 2012, pp. 350-353. doi: 10.4236-am.2012.34054.





Author: Francisco Louzada, Estela M. P. Bereta, Maria A. P. Franco

Source: http://www.scirp.org/



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