A New Inverse Rayleigh Distribution with Applications of COVID-19 Data: Properties, Estimation Methods and Censored Sample

This paper aims at modelling the COVID-19 spread in the United Kingdom and the United States of America, by specifying an optimal statistical univariate model. A new lifetime distribution with three-parameters is introduced by a combination of inverse Rayleigh distribution and odd Weibull family of distributions to formulate the odd Weibull inverse Rayleigh (OWIR) distribution. Some of the mathematical properties of the OWIR distribution are discussed as linear representation, quantile, moments, function of moment production, hazard rate, stress-strength reliability, and order statistics. Maximum likelihood, maximum product spacing, and Bayesian estimation method are applied to estimate the unknown parameters of OWIR distribution. The parameters of the OWIR distribution are estimated under the progressive type-II censoring scheme with random removal. A numerical result of a Monte Carlo simulation is obtained to assess the use of estimation methods.