Abstract
In Statistical theory, inclusion of an additional parameter to standard distributions is a usual practice. In this study, a new distribution referred to as Alpha-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution, including moment generating function, mode, quantiles, entropies, mean residual life function, stochastic orders and order statistics are obtained. Parameters of the proposed distribution have been estimated using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that the proposed distribution outperforms different variants of Pareto distribution on the basis of model selection criteria.
Highlights
For the last few decades, improvement over standard distributions has become a common practice in statistical theory
The aim of this study is to propose a new and more flexible distribution, which, we call Alpha Power Pareto (APP) distribution, by introducing an additional parameter to Basic Pareto distribution, to obtain an adequate fit
Assuming that X is a continuous random variable with survival function given in Eq (8), the mean residual life function is defined as the expected additional lifetime that a component has survived until time t
Summary
OPEN ACCESS Citation: Ihtisham S, Khalil A, Manzoor S, Khan SA, Ali A (2019) Alpha-Power Pareto distribution: Its properties and applications. In Statistical theory, inclusion of an additional parameter to standard distributions is a usual practice. A new distribution referred to as Alpha-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution, including moment generating function, mode, quantiles, entropies, mean residual life function, stochastic orders and order statistics are obtained. Parameters of the proposed distribution have been estimated using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that the proposed distribution outperforms different variants of Pareto distribution on the basis of model selection criteria
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