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Exponentiated exponential family: An alternative to gamma and Weibull distributions. (English) Zbl 0997.62076
Summary: We study the properties of a new family of distributions, namely exponentiated exponential distributions, by R.C. Gupta, R.D. Gupta and P.L. Gupta [Commun. Stat., Theory Methods 27, No. 4, 887-904 (1998)]. The exponentiated exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed, that many properties of this new family are quite similar to those of a Weibull or gamma family, therefore this distribution can be used as a possible alternative to a Weibull or gamma distribution.
We present two real life data sets, where it is observed that in one data set exponentiated exponential distribution has a better fit compared to the Weibull or gamma distribution and in the other data set Weibull has a better fit than the exponentiated exponential or gamma distribution. Some numerical experiments are performed to see how the maximum likelihood estimators and their asymptotic results work for finite sample sizes.

MSC:
62N02 Estimation in survival analysis and censored data
60E15 Inequalities; stochastic orderings
62E10 Characterization and structure theory of statistical distributions
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