Journal de biométrie et biostatistique

Statistical Inference of Kumaraswamy Distribution under Imprecise Information

Abstract

Indranil Ghosh

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. Furthermore, we provide an approximation namely, Tierney and Kadane’s approximation, to compute the Bayes estimates of the unknown parameters. 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.