Half Logistic Generalized Rayleigh Distribution for Modeling Hydrological Data

This article introduced a three-parameter extension of the Generalized Rayleigh distribution called half-logistic Generalized Rayleigh distribution, which has submodels the Generalized Rayleigh and Rayleigh distribution. The proposed model is quite flexible and adaptable to model any kind of life-time data. Its probability density function may sometimes be unimodal and its corresponding hazard rate may be of monotone or non-monotone shape. Standard statistical properties such as it ordinary and incomplete moments, quantile function, moment generating function, reliability function, stochastic ordering, order statistics, Renyi, and \({\varvec{\delta}}\) $\mathit{\delta }$ -entropy are obtained. The maximum likelihood method is used to obtain the estimates of the model parameters. Two practical examples of hydrological data sets are presented.