The Length–Biased Weibull–Rayleigh Distribution for Application to Hydrological Data

Abstract

Abstract: In this study, we introduce a new class of length–biased distribution, the length–biased Weibull–Rayleigh (LBWR) distribution, and provide its properties such as the limit behavior, survival function, hazard rate function, rth moment, and moment generating function. Moreover, maximum likelihood estimation is used in the parameter estimation. The LBWR distribution was fitted to two hydrological datasets and its efficacy compared with Rayleigh, Weibull, Pareto, and Weibull–Rayleigh distributions, the results of which show that the novel distribution provides a better fit than the others.