On Size Biased Kumaraswamy Distribution

TL;DR

This paper introduces the size-biased Kumaraswamy distribution, explores its properties, estimates its parameters using maximum likelihood and quantile methods, and applies it to real and simulated data.

Contribution

It presents the novel size-biased Kumaraswamy distribution and analyzes its properties, estimation methods, and practical applications.

Findings

Distributional properties are thoroughly studied.

Maximum likelihood and quantile estimation methods are developed.

The model is successfully applied to real and simulated data.

Abstract

In this paper, we introduce and study the size-biased form of Kumaraswamy distribution. The Kumaraswamy distribution which has drawn considerable attention in hydrology and related areas was proposed by Kumarswamy. The new distribution is derived under size-biased probability of sampling taking the weights as the variate values. Various distributional and characterizing properties of the model are studied. The methods of maximum likelihood and matching quantiles estimation are employed to estimate the parameters of the proposed model. Finally, we apply the proposed model to simulated and real data sets.