On the lifetime as the maximum or minimum of the sample with power series distributed size

Abstract

The present paper treats the topic of the distribution of the maximum and minimum of a sequence of an independent identically distributed random variables (i.i.d.r.v.) in a random number in a unitary manner and from the perspective of the power series distribution class. The general formulas are obtained, and by using concrete examples, they lead to some of the distributions obtained by Adamidis and Loukas (1998), Kus (2007), Tahmasbi and Rezaei (2008), Leahu and Lupu (2010), Baretto-Souza, Morais and Cordeiro (2011), Morais and Baretto-Souza (2011), Cancho, Louzada and Barriga (2011), Louzada, Roman and Cancho (2011), Flores, Borges, Cancho and Louzada (2013). Examples of new distributions are also presented.