The beta-Pareto distribution

Abstract

In this paper, a four-parameter beta-Pareto distribution is defined and studied. Various properties of the distribution are discussed. The distribution is found to be unimodal and has either a unimodal or a decreasing hazard rate. The expressions for the mean, mean deviation, variance, skewness, kurtosis and entropies are obtained. The relationship between these moments and the parameters are provided. The method of maximum likelihood is proposed to estimate the parameters of the distribution. The distribution is applied to two flood data sets.

Keywords:

• unimodality
• hazard function
• moments
• estimation
• flood peaks

AMS Classification :

• 60E05
• 62F10
• 62P99

Acknowledgements

The authors express their gratefulness to the referees for valuable comments and suggestions which have enhanced the paper.