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A Generalization of Generalized Gamma Distributions


Generalized gamma distribution, Generalized gamma function, Generalized Beta II distribution, Maximum likelihood estimation.


For the first time, a new generalization of generalized gamma distribution called the modified generalized gamma distribution has been introduced to provide greater flexibility in modeling data from a practical viewpoint. The new distribution generalizes some recently introduced generalizations of the gamma distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean deviation, mean residual lifetime and expression of the entropies are derived. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Two real data sets have been analyzed to show how the proposed models work in practice.





Pakistan Journal of Statistics and Operation Research; Vol. 14 No. 1, 2018

Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810