Abstract
In this article we propose and study the so-called beta exponential Pareto (BEP) distribution. Several lifetime distributions such as the beta Weibull, beta exponential, beta Rayleigh, generalized Weibull, Weibull among others are embedded in the proposed distribution. Various mathematical properties of the BEP distribution are presented. We also discuss the parameter estimation methods and simulation issues. The importance and flexibility of the proposed model are illustrated by means of real data analysis.
Highlights
The Pareto distribution is well known in the literature for its capability of modeling heavy-tailed data
As we shall see both pdf and cdf of beta exponential Pareto (BEP) distribution can be expressed in terms of the exponential Pareto distribution
Several methods for parameter estimation have been proposed in the literature but the maximum likelihood estimation (MLE) method is commonly used as the MLEs are usually unbiased and have minimum variance
Summary
The Pareto distribution is well known in the literature for its capability of modeling heavy-tailed data. The Pareto distribution has a scale parameter which acts as a threshold value of the observations. This means Pareto distribution could be used only if it takes positive values greater than the threshold parameter This restriction has limited the usefulness of the Pareto distribution. BEP will have five parameters, the main advantage of this formulation is that the support of the proposed distribution is (0, ∞) which adds versatility and applicability to model data under study.
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