On a new generalization of Pareto distribution and its applications

Abstract

Pareto distribution is one of the well known distributions used to fit heavy-tailed data. Various generalizations of this distribution have been reported in the literature by several authors. An obvious reason for generalizing a standard distribution is that the generalized form provides greater flexibility in modeling real data. In this article, we introduce a new four parameter distribution called New Generalized Pareto distribution, which is a generalization of the classical Pareto distribution. The structural properties of the new distribution are discussed. It is shown that the distribution is heavy-tailed and belongs to the class of subexponential distributions. Certain characterizations of the new distribution are obtained. We also derive the distribution of order statistics. The method of maximum likelihood is used for estimating the model parameters. We provide simulation results to assess the performance of the maximum likelihood estimates of the model parameters. Autoregressive time series model with the new generalized Pareto distribution as marginal is developed. An application of a real data set shows the performance of the new distribution over other generalizations of Pareto distribution.

Keywords:

• Autoregressive Time Series Models
• Characterizations
• Hazard Rate
• Maximum Likelihood Estimate
• Order Statistics
• Pareto distribution
• Rényi Entropy
• Shannon Entropy

2000 AMS Classification:

• 60E05
• 62E10
• 62P99

Disclosure statement

No potential conflict of interest was reported by the authors.