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Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions
Author(s) -
Gupta Rameshwar D.,
Kundu Debasis
Publication year - 2001
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/1521-4036(200102)43:1<117::aid-bimj117>3.0.co;2-r
Subject(s) - weibull distribution , exponentiated weibull distribution , gamma distribution , mathematics , natural exponential family , exponential family , generalized gamma distribution , exponential function , estimator , statistics , exponential distribution , shape parameter , mathematical analysis
In this article we study some properties of a new family of distributions, namely Exponentiated Exponential distribution, discussed in Gupta , Gupta , and Gupta (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 a gamma family, therefore this distribution can be used as a possible alternative to a Weibull or a 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 Weibull or gamma distribution and in the other data set Weibull has a better fit than 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.