Estimation of the Rayleigh distribution parameters with presence of k outliers generated from Gamma distribution

Abstract

The moment, maximum likelihood and mixture of the estimators of parameters of the Rayleigh distribution are derived with presence of k outliers generated from Gamma distribution. These estimators are compared empirically when all the parameters are unknown; their Bias and MSE are investigated with the help of numerical technique. We have shown that these estimators are asymptotically unbiased. At the end, we conclude that mixture estimators are better than the maximum likelihood and moment estimators.   Key words: Rayleigh distribution, mixture estimators, outliers, Newton-Raphson method.