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.

💡 Research Summary

The paper introduces the Beta Generalized Exponential (BGE) distribution, a four‑parameter family that subsumes both the Beta Exponential (BE) and the Generalized Exponential (GE) distributions as special cases. The authors define the BGE density as

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