The extended gamma distribution with regression model and applications
Citation
Altun, E., Korkmaz, M. Ç., El-Morshedy, M., & Eliwa, M. S. (2021). The extended gamma distribution with regression model and applications [J]. AIMS Mathematics, 6(3), 2418-2439.Abstract
This paper introduces a new extension of the gamma distribution, named as a new extended
gamma distribution, via mixture representation of xgamma and gamma distributions. The statistical
properties of the proposed distribution are derived such as moment generating and characteristic
functions, variance, skewness, and kurtosis measures, Lorenz curve, and mean residual life function.
The maximum likelihood, parametric bootstrap, method of moments, least squares, and weighted
least squares estimation methods are considered to obtain the unknown model parameters. The finite
sample performance of estimation methods is discussed via a simulation study. Using the proposed
distribution, we propose a new regression model for the right-skewed response variable as an alternative
to the gamma regression model. Two real data sets are analyzed to convince the readers for the
usefulness of the proposed model.