Statistical Inference of Kumaraswamy distribution under imprecise information

TL;DR

This paper develops methods for estimating the parameters of the Kumaraswamy distribution when data is imprecise and fuzzy, using maximum likelihood, Newton Raphson, and EM algorithms, with comparisons via simulations.

Contribution

It introduces a novel approach for parameter estimation of the Kumaraswamy distribution under fuzzy information, extending traditional methods to imprecise data.

Findings

EM algorithm performs well in bias reduction

Newton Raphson converges faster with precise initial guesses

Simulation results show the proposed methods are effective

Abstract

Traditional statistical approaches for estimating the parameters of the Kumaraswamy distribution have dealt with precise information. However, in real world situations, some information about an underlying experimental process might be imprecise and might be represented in the form of fuzzy information. In this paper, we consider the problem of estimating the parameters of a univariate Kumaraswamy distribution with two parameters when the available observations are described by means of fuzzy information. We derive the maximum likelihood estimate of the parameters by using Newton Raphson as well as EM algorithm method. The estimation procedures are discussed in details and compared via Markov Chain Monte Carlo simulations in terms of their average biases and mean squared errors.