Highest posterior density estimation for Burr X model based on fuzzy data

Classical estimation techniques for the parameter of Burr X distribution are dealing with precise observations. However, in real world situations, the results of an experimental performance cannot always be recorded or measured precisely, but each observable event may only be identified with a fuzzy subset of the sample space. Therefore, the conventional procedures used for estimating the parameter of Burr Xmodel will have to be adapted to the new situation. In this paper, we develop the highest posterior density (HPD) estimation for Burr X distribution when the available observations are described in terms of fuzzy numbers. Because there are not closed forms for the posterior equations, we use Newton-Raphson algorithm to compute the HPD estimates. Monte Carlo simulations are performed in order to assess theaccuracy of the proposed method.

Keywords:

Highest posterior density estimation , Fuzzy data , Monte Carlo simulation , Burr X model.