Geodesic
A weighted version of Gamma distribution
Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 89-111

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Weighted Gamma (WG), a weighted version of Gamma distribution, is introduced. The hazard function is increasing or upside-down bathtub depending upon the values of the parameters. This distribution can be obtained as a hidden upper truncation model. The expressions for the moment generating function and the moments are given. The non-linear equations for finding maximum likelihood estimators (MLEs) of parameters are provided and MLEs have been computed through simulations and also for a real data set. It is observed that WG fits better than its submodels (WE), Generalized Exponential (GE), Weibull and Exponential distributions.
Keywords: gamma distribution, weight function, hazard function, maximum likelihood estimator, Akaike Information criterion 
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Jain, Kanchan; Singla, Neetu; Gupta, Rameshwar. A weighted version of Gamma distribution. Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 89-111. http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a6/