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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 FrĂ©chet 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.

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