The Generalized Odd Generalized Exponential Family of Distributions: Properties, Characterizations and Application

Morad Alizadeh ； Indranil Ghosh ； Haitham M. Yousof ； Mahdi Rasekhi ； G.G.Hamedani

《Journal of Data Science》 15卷3期 (2017/07) Pp. 443-465

https://doi.org/10.6339/JDS.201707_15(3).0005

摘要

We introduce a new class of distributions called the generalized odd generalized exponential family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi, Shannon and q-entropies, order statistics and probability weighted moments are derived. We also propose bivariate generalizations. We constructed a simple type Copula and intro-duced a useful stochastic property. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors via a simulation study.

關鍵字

Characterizations ； Generalized Odd Generalized exponential-G Family ； Generating Function ； Maximum Likelihood Estimation ； Moments ； Quantile function