Compare Some Shrinkage Bayesian Estimation Method forGumbel-Max Distribution with Simulation

Abstract

     The Gumbel max distribution is one of the most important statistical distributions because it has many applications, especially in the field of water research and the prediction of earthquakes and volcanoes. This work includes a comparison of several Shrinkage Bayesian methods, namely the Shrinkage Bayesian Square Loss Function, Shrinkage Bayesian Lenix Function, and Shrinkage Bayesian Unix Function to estimate the distribution parameter. The research also includes several simulated experiments according to the sample size change and the real value of the distribution parameter. The number of experiments is 15 simulated experiments based on the difference sample size and true distribution parameter values. The results of the simulation experiments are compared depending on each of the absolute least difference criteria (  and the mean squared error (). The comparison results show that the estimation method is affected by the sample size, and the real value of the distribution parameter. The best estimation method is the Shrinkage Bayesian Lenix Function. The Bayesian methods can be applied to other statistical distributions such that the Lindley Weibull distribution and logistics distribution.