A Review of the Rayleigh Distribution: Properties, Estimation & Application to COVID-19 Data

We study the different properties of the Rayleigh distribution. These include the descriptive properties, reliability properties and stochastic orders. Next, we consider seven different estimation methods for estimating the parameter, namely: maximum likelihood estimation, matching moments estimation, maximum product of spacing estimation, ordinary least squares estimation, Cramer-von Mises estimation, Anderson-Darling estimation and right-tail Anderson-Darling estimation. A simulation study is done to assess the performance of these methods of estimation and the results shows that all the estimators are mostly efficient and consistent. Finally, using the method of maximum likelihood estimation, we demonstrate the applicability of the Rayleigh distribution by modelling the Netherlands's COVID-19 mortality rate data as an example.