Bias Reduction for the Maximum Likelihood Estimator of the Parameters of the Generalized Rayleigh Family of Distributions

Abstract

We derive analytic expressions for the biases, to O(n^{− 1}), of the maximum likelihood estimators of the parameters of the generalized Rayleigh distribution family. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and generally results in a small reduction in relative mean squared error. In general, the analytic bias-corrected estimators are also found to be superior to the alternative of bias-correction via the bootstrap.

Keywords:

• Generalized Rayleigh distribution
• Maximum likelihood
• Bias
• Mean squared error
• Bias correction.

Mathematics Subject Classification:

• 62F10
• 62G09
• 62P20.