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Theory & Methods: Generalized exponential distributions
Author(s) -
Gupta Rameshwar D.,
Kundu Debasis
Publication year - 1999
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00072
Subject(s) - weibull distribution , shape parameter , mathematics , scale parameter , gamma distribution , exponentiated weibull distribution , generalized gamma distribution , generalized integer gamma distribution , natural exponential family , exponential function , exponential family , weibull modulus , location parameter , exponential distribution , k distribution , distribution (mathematics) , generalized beta distribution , statistics , hazard , statistical parameter , probability distribution , distribution fitting , mathematical analysis , chemistry , organic chemistry
The three‐parameter gamma and three‐parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three‐parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three‐parameter generalized exponential distribution fits better than the three‐parameter Weibull distribution or the three‐parameter gamma distribution.