Estimation of Parameters of the Two-Parameter Rayleigh Distribution

In this book, Maximum likelihood estimates for the shape and scale parameters of Two- Parameters Rayleigh distribution are obtained based on progressive type-II censored samples using the Newton-Raphson (NR) method and the Expectation-maximization (EM) algorithm. A simple algorithm of Balakrishnan and Sandhu (1995) and Aggarwala and Balakrishnan (2000) is used for generating progressive type-II censored samples. Based on this censoring scheme, approximate asymptotic variances are derived and used to construct approximate confidence intervals of the parameters. The performance of these two maximum likelihood estimation methods is compared through simulation results of biases, root mean squared error (RMSE), and the coverage rate. Simulation results showed that in nearly all the combination of simulation conditions the estimators based on the EM algorithm have small biases, small variances, the small root of mean squared error, and narrower widths of confidence intervals compared to those obtained using the NR method. Finally, two illustrative examples with real-life data sets are provided to illustrate how maximum likelihood estimation using the two algorithms works in practice.