@article{Monem_2022, title={Review on the Inverse Rayleigh Distribution}, volume={6}, url={http://ajms.in/index.php/ajms/article/view/407}, DOI={10.22377/ajms.v6i1.407}, abstractNote={<p>This article discusses Bayesian and non-Bayesian estimation problem of the unknown parameter for the inverse Rayleigh distribution based on the lower record values. Maximum likelihood estimators of the unknown parameters were obtained. Furthermore, Bayes estimator has been developed under squared error and zero one loss functions. We discuss also statistical properties and estimation of power-transmuted inverse Rayleigh distribution (EIRD). We introduce the transmuted modified inverse Rayleigh distribution using quadratic rank transmutation map, which extends the modified inverse Rayleigh distribution. We introduce a generalization of the inverse Rayleigh distribution known as EIRD which extends a more flexible distribution for modeling life data. Some statistical properties of the EIRD are investigated, such as mode, quantiles, moments, reliability, and hazard function. We describe different methods of parametric estimations of EIRD discussed by using maximum likelihood estimators, percentile-based estimators, least squares estimators, and weighted least squares estimators and compare those estimates using extensive numerical simulations. The new two-scale parameters generalized distribution were studies with its distribution and density functions, besides that the basic properties such as survival, hazard, cumulative hazard, quantile function, skewness, and Kurtosis functions were established and derived. To estimate the model parameters, maximum likelihood, and rank set sampling estimation methods were applied with real-life data. We have introduced weighted inverse Rayleigh (WIR) distribution and investigated its different statistical properties. Expressions for the Mode and entropy have also been derived. A comprehensive account of the mathematical properties of the modified inverse Rayleigh distribution including estimation and simulation with its reliability behavior is discussed.</p>}, number={1}, journal={Asian Journal of Mathematical Sciences(AJMS)}, author={Monem, Amel Abd-El-}, year={2022}, month={Jun.} }