Bayesian estimation for Rayleigh distribution based on ranked set sampling

Abstract

The Rayleigh distribution is an important model in applications such as noise theory, height of the sea waves and wave length. In this paper, we provide Bayesian estimation for a parameter of the Rayleigh distribution based on simple random sample (SRS) and ranked set sampling (RSS) and maximum ranked set sampling procedure with unequal samples (MRSSU) in two cases, one cycle and m-cycle. We also obtain the Bayes estimators by using square-root inverted-gamma and Jeffreys prior under squared error loss function and general entropy loss function and LINEX function. Finally, we compute the bias and mean squared error of an estimator under squared error and compare its with the corresponding RSS and MRSSU through Monte Carlo simulations.