Efficient Estimation of the Density and Cumulative Distribution Function of the Generalized Rayleigh Distribution

Abstract

The uniformly minimum variance unbiased (UMVU), maximum likelihood, percentile (PC), least squares (LS) and weighted least squares (WLS) estimators of the probability density function (pdf) and cumulative distribution function are derived for the generalized Rayleigh distribution. This model can be used quite effectively in modelling strength data and also modelling general lifetime data. It has been shown that MLE is better than UMVUE and UMVUE is better than the others. An application to waiting times (min) of 100 bank customers.