A new generalization of the normal distribution: the gamma-normal distribution and its applications

Statistical distributions are commonly applied to describe real world phenomena. Due to the usefulness of statistical distributions, their theory is widely studied and new distributions are developed. The interest in developing more flexible statistical distributions remains strong in statistics profession. Many generalized classes of distributions have been developed and applied to describe various phenomena. Recently, Alzaatreh et al. (2014) developed a new method to generate family of distributions and called it the gamma-X family of distributions

A new generalization of the normal distribution: the gamma-normal distribution and its applications

Statistical distributions are commonly applied to describe real world phenomena. Due to the usefulness of statistical distributions, their theory is widely studied and new distributions are developed. The interest in developing more flexible statistical distributions remains strong in statistics profession. Many generalized classes of distributions have been developed and applied to describe various phenomena. Recently, Alzaatreh et al. (2014) developed a new method to generate family of distributions and called it the gamma-X family of distributions

The Beta Generalized Exponential Distribution

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the $r$th moment thus generalizing some results in the literature. Expressions for the density, moment generating function and $r$th moment of the order statistics also are obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix. We observe in one application to real data set that this model is quite flexible and can be used quite effectively in analyzing positive data in place of the beta exponential and generalized exponential distributions