Comparison between least squares and percentile methods in estimating Rayleigh Kumaraswamy distribution, a simulation study

Abstract

In this research, a new generalization of the Rayleigh distribution called the Rayleigh-Kumaraswamy distribution was introduced. The extended formulas for the probability density function (PDF) and cumulative distribution function (CDF) were derived. Furthermore, some uses of distribution properties such as moments and moments generating function were also derived. The PDF property of the distribution was preserved. Additionally, A simulation study was conducted using different sample sizes and various assume .Two different methods for estimating the parameters of the new distribution are presented: the least squares method, and the method based on percentiles. Simulation studies are conducted to compare the performance of these estimation methods using different sample sizes and assumed parameter values. The comparison is based on statistical criteria such as mean square error and bias. The results indicate that the least squares method performs the best