Estimation fuzzy Bayes estimation of the risk function of a truncated Cauchy distribution with practical application

Abstract

In this research, the focus was on the robust fuzzy Bayesian methods to find the estimators of the risk function and some of its indicators for the two-parameter truncated Cauchy distribution. Its estimates using a similar Squared Error Loss Function, the simulation method was employed using the (Monte-Carlo) method to generate random data for a sample of six different sizes (15-25-35-50-75-100) following the truncated Cauchy distribution With two parameters, and depending on the simulation results and using the statistical mean square error (MSE) criterion as a statistical criterion for comparison, the preference of the impartial fuzzy informational standard Bayes estimator appeared under the quadratic loss function for medium and large sample sizes to estimate the risk function over other estimation methods. The study was conducted on a real sample of (100) observations representing ECG failure times in months. The study concluded that the estimation methods used in the applied side give appropriate and accurate estimates for the study data and agree with what was reached in the experimental side.