R. Tahmasbi and S. Rezaei, “A Two-Parameter Life-Time Distribution with Decreasing Failure Rate,” Computational Statistics and Data Analysis, Vol. 52, No. 8, 2008, pp. 3889-3901. doi:10.1016/j.csda.2007.12.002

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).