A comparison study between Bayesian robustness estimation and numerical methods for the scale parameter of the Rayleigh distribution

Abstract

This paper uses robust statistical estimating techniques and the numerical methods to estimate and approximate the scale parameter of the Rayleigh distribution under complete data. Robust Bayes analysis depends on (unbalanced and balanced) loss functions based on (ML-II-ϵ-contaminated class and derived under the prior contaminant distribution of the Frechet distribution and the approximate values numerically are finding by using three numerical methods (Newton-Raphson method, false position method, and the secant method). The estimators' performances were contrasted according to simulation experiments for different cases and sample sizes depending on the value for the mean squared error.