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

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DOI: 10.4236/am.2012.34054    6,376 Downloads   10,477 Views   Citations

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).

Conflicts of Interest

The authors declare no conflicts of interest.

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.

References

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