Estimating the parameters of Lomax distribution from imprecise information

Abstract

Traditional statistical approaches for estimating the parameters of Lomax distribution have dealt with precise information. However, in real world situations, some information about an underlying system might be imprecise and are represented in the form of fuzzy information. In this paper, we consider the problem of estimating the parameters of Lomax distribution when the available observations are described by means of fuzzy information. We obtain the maximum likelihood estimate of the parameters by using the Newton-Raphson as well as the EM algorithm. We also 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 Monte Carlo simulations in terms of their estimated biases and mean squared errors. Finally, analysis of one data set is provided for the purpose of illustration.

Keywords

• Imprecise data
• Fuzzy information
• Lomax distribution
• Maximum likelihood estimation
• Bayesian estimation