Estimating the Parameters of Burr Type XII Distribution with Fuzzy Observations

Abstract

In this article, the classical as well as the Bayesian estimation problems of two-parameter Burr type XII distribution based on fuzzy data are considered. The maximum likelihood estimators via two methods, namely, Newton-Raphson and Expectation-Maximization algorithms are computed. The standard errors of the estimates are computed using the observed information matrix. For computing the Bayes estimators, three methods viz Lindley’s approximation, Tierney-Kadane approximation and highest posterior density method are obtained. Monte-Carlo simulation experiments are conducted to investigate the performance of the proposed methods. Finally, the proposed methods are illustrated by using three different real data sets.

Keywords

• Bayesian estimation
• Burr type XII distribution
• expectation-maximization algorithm
• fuzzy observations
• Lindley’s approximation
• maximum likelihood estimation