The exponentiated type distributions. (English) Zbl 1128.62015

Summary: R. C. Gupta et al. [Commun. Stat., Theory Methods 27, No. 4, 887–904 (1998; Zbl 0900.62534)] introduced the exponentiated exponential distribution as a generalization of the standard exponential distribution. We introduce four more exponentiated type distributions that generalize the standard gamma, standard Weibull, standard Gumbel and the standard Fréchet distributions in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. A treatment of the mathematical properties is provided for each distribution.


62E10 Characterization and structure theory of statistical distributions
62E15 Exact distribution theory in statistics
33C90 Applications of hypergeometric functions


Zbl 0900.62534
Full Text: DOI


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