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Transmuted gamma-mixed Rayleigh distribution: Properties and estimation with bladder cancer data example

In this article, we generalize the gamma mixed Rayleigh distribution using the quadratic rank transmutation map studied by Shaw et al. [38] to develop a transmuted gamma mixed Rayleigh (TGMR) distribution. We provide a comprehensive description of the mathematical and statistical properties of the subject distribution. We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, percentile based estimators, least squares estimators, method of maximum product of spacings, method of Cramér-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling. Finally, a real data analysis is carried out to illustrate the superiority of the proposed distribution.