Robust estimation of Weibull-Rayleigh parameters

Weibull-Rayleigh distribution is one important compound distributions that has been proposed recently. The maximum likelihood estimator can be used to estimate parameters of the mathematical distributions. However, this estimator is highly sensitive to outliers. Researchers propose to use robust methods to estimate the parameters instead of maximum likelihood estimator when the data has outliers. To date, no work has been conducted to suggest a robust method for estimating parameters of Weibull-Rayleigh when the data has outliers. The M-Estimator method is one of the robust methods that is widely used to estimate the parameters. Therefore, the conventional M-Estimator method is extended to estimate the parameters of Weibull-Rayleigh distribution when the data has outliers . Results show that the performance of M-Estimator is more efficient than the MLE at different contamination percentages.