A New Extended Rayleigh Distribution with Applications of COVID-19 Data

In this manuscript, we proposed a new extension of the Rayleigh distribution named as MTI Rayleigh distribution (MTIRD) that provides better fits than the Rayleigh distribution and some of its known generalizations. Various properties of the proposed distribution, including moments, moment generating function, hazard rate, conditional moments, Bonferroni and Lorenz curve, mean residual life, mean waiting time, Renyi entropy and order statistics are derived. Maximum likelihood estimation procedure is employed to estimate the unknown parameters. An extensive simulation study is carried out to illustrate the behaviour of MLEs on the basis of Mean Square Errors. The flexibility of the new distribution is assessed by applying it to two real data sets of COVID-19 mortality. The comparative behaviour of MTIRD with Rayleigh distribution, Power Rayleigh distribution, Transmuted Rayleigh distribution, Exponentiated Rayleigh distribution, Weibull Rayleigh distribution provided the evidence that it outperforms the other competing distributions based on Akaike Information Criterion, Bayesian Information Criterion, Akaike Information criterion Corrected, and other goodness of fit measures.