Comparing Bayes estimation with Maximum Likelihood Estimation of Generalized Inverted Exponential Distribution in Case of Fuzzy Data

Abstract

Abstract: In this paper, the generalized inverted exponential distribution is considered as one of the most important distributions in studying failure times. A shape and scale parameters of the distribution have been estimated after removing the fuzziness that characterizes its data because they are triangular fuzzy numbers. To convert the fuzzy data to crisp data the researcher has used the centroid method. Hence the studied distribution has two parameters which show a difficulty in separating and estimating them directly of the MLE method. The Newton-Raphson method has been used.For the Bayesian method, the gamma distribution has been proposed as a prior distribution for the two parameters with a quadratic loss function and by using Metropolis-Hasting algorithm to find the Bayesian parameters estimators. Different samples have been generated to represent the population under study by using simulation approach. After estimating the parameters, the results of the two methods have been compared according to the Mean Squared Error measurement. And the researcher concluded that the best estimation method is the MLE followed by the Bayesian.