Abstract
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.
Highlights
The statistical literature contains many new classes of distributions that have been constructed by extending the common families of continuous distributions providing more flexibility as far as applications is concerned
Several classes of distributions have been constructed by extending common families of continuous distributions. These generalized distributions give more flexibility by adding new parameters to the baseline model. These methods were pioneered by Gupta et al (1998) who proposed the exponentiated-G class, which consists of raising the cumulative distribution function to a positive power parameter
We propose and study a new generated family called the Generalized Odd Generalized Exponential-G (GOGE-G) family via the T-X family defined by Alzaatreh et al (2013) and give a comprehensive description of its mathematical properties
Summary
The statistical literature contains many new classes of distributions that have been constructed by extending the common families of continuous distributions providing more flexibility as far as applications is concerned. These new families have been used for modeling data in many applied areas such as engineering, economics, biological studies and environmental sciences. Several classes of distributions have been constructed by extending common families of continuous distributions These generalized distributions give more flexibility by adding new parameters to the baseline model. The plots of pdf and hrf for some special cases of GOGE-G are given in Figuers 1-4
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