A New Generalized Odd Gamma Uniform Distribution: Mathematical Properties, Application and Simulation

Abstract

n many applied areas there is a clear need for the extended forms of the well-known distributions.The new distributions are more flexible to model real data that present a high degree of skewness and kurtosis, such that each one solves a particular part of the classical distribution problems. In this paper, a new two-parameter Generalized Odd Gamma distribution, called the (GOGaU) distribution, is introduced and the fitness capability of this model are investigated. Some structural properties of the new distribution are obtained. The different methods including: Maximum likelihood estimators, Bayesian estimators (posterior mean and maximum a posterior), least squares estimators, weighted least squares estimators, Cramér-von-Mises estimators, Anderson-Darling and right tailed Anderson-Darling estimators are discussed to estimate the model parameters. In order to perform the applications, the importance and flexibility of the new model are also illustrated empirically by means of two real data sets. For simulation Stan and JAGS software were utilized in which we have built the GOGaU JAGS module