Author(s)

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

Department of Applied Maths & Statistics, ICMC, Universidade de S?o Paulo, S?o Paulo, Brazil.
Department of Statistics, CCET, Universidade Federal de S?o Carlos, S?o Carlos, Brazil.

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 Y_i,{i = 1,2,…,N} is obtained if one compounds the probability generating function of N with the survival or the distribution func-tion of Y_i. 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).

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

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.