An Estimation of Survival and Hazard Functions of Weighted Rayleigh Distribution

Abstract

In this paper, we introduce a new class of Weighted Rayleigh Distribution based on two parameters, one is the scale parameter and the other is the shape parameter introduced in Rayleigh distribution. The main properties of this class are derived and investigated The Moment method (ME) and the Maximum Likelihood method (MLE) are used to obtain estimators of parameters of this distribution. The probability density function, survival function, cumulative distribution and hazard function are derived and found. Real data sets are collected to investigate the two methods applied in this study. A comparison was made between the two methods of estimation and it is clear that MLE is better than ME according to the results of the mean squares error.