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General results for the Marshall and Olkin’s family of distributions. (English) Zbl 1285.62014

Summary: A.W. Marshall and I. Olkin [Biometrika, No.3, 641–652 (1997, Zbl 0888.62012)] introduced an interesting method of adding a parameter to a well-established distribution. However, they did not investigate the general mathematical properties of their family of distributions. We provide for this family of distributions general expansions for the density function, explicit expressions for the moments and the moments of the order statistics. Several especial models are investigated. We discuss estimation of the model parameters. An application to a real data set is presented for illustrative purposes.

MSC:

62E10 Characterization and structure theory of statistical distributions
62G30 Order statistics; empirical distribution functions
62F10 Point estimation
65C05 Monte Carlo methods

Citations:

Zbl 0888.62012

Software:

Ox
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References:

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