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Marshall-Olkin generalized exponential distribution. (English) Zbl 1329.62068

Summary: A. W. Marshall and I. Olkin [Biometrika 84, No. 3, 641–652 (1997; Zbl 0888.62012)] introduced a new way of incorporating a parameter to expand a family of distributions. In this paper we adopt the Marshall-Olkin approach to introduce an extra shape parameter to the two-parameter generalized exponential distribution. It is observed that the new three-parameter distribution is very flexible. The probability density functions can be either a decreasing or an unimodal function. The hazard function of the proposed model, can have all the four major shapes, namely increasing, decreasing, bathtub or inverted bathtub types. Different properties of the proposed distribution have been established. The new family of distributions is analytically quite tractable, and it can be used quite effectively, to analyze censored data also. Maximum likelihood method is used to compute the estimators of the unknown parameters. Two data sets have been analyzed, and the results are quite satisfactory.

MSC:

62E10 Characterization and structure theory of statistical distributions
62F10 Point estimation
62G30 Order statistics; empirical distribution functions
62P10 Applications of statistics to biology and medical sciences; meta analysis

Citations:

Zbl 0888.62012
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References:

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