Open AccessThe extended gamma distribution with regression model and applications
Author(s) -
Emrah Altun,
Mustafa Ç. Korkmaz,
Mahmoud El-Morshedy,
Mohamed S. Eliwa
Publication year - 2020
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2021147
Subject(s) - mathematics , kurtosis , skewness , gamma distribution , statistics , moment (physics) , parametric statistics , distribution (mathematics) , generalized gamma distribution , mathematical analysis , physics , classical mechanics
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.