K. Adamidis and S. Loukas, “A Lifetime Distribution with Decreasing Failure Rate,” Statistics and Probability Letters, Vol. 39, No. 1, 1998, pp. 35-42. doi:10.1016/S0167-7152(98)00012-1

has been cited by the following article:

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

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

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

  JOURNAL NAME: Applied Mathematics, Vol.3 No.4, April 27, 2012

  ABSTRACT: 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).