Introducing a New Unit Gamma Distribution: Properties and Applications

Abstract

This article fills a gap in distribution theory and statistics by introducing a new, simple and intuitive two-parameter unit distribution derived from the gamma distribution. It serves as a complementary option to the existing unit gamma distribution. The main features are explored through both theoretical and practical approaches. Specifically, the shapes of the corresponding probability density and hazard rate functions are studied, an understandable stochastic comparison with the existing unit gamma distribution is provided, moments and incomplete moments are expressed, moment skewness and kurtosis are computed, random numbers are generated, and a new family of distributions is proposed. A statistical application demonstrates how the two parameters can be estimated quite effectively and the fit to a real data set is tested. It is also shown that the new distribution is able to outperform four well-known two-parameter unit distributions: the beta distribution, the Kumaraswamy distribution, the unit Weibull distribution and, more importantly, the existing unit gamma distribution. An appendix lists the main codes used in the application.