The Length–Biased Weibull–Rayleigh Distribution for Application to Hydrological Data
Tanachot Chaito, Manad Khamkong
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, $$r$$ th 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.
Topics & Concepts
Weibull distributionMathematicsRayleigh distributionExponentiated Weibull distributionStatisticsRayleigh scatteringMoment (physics)Distribution (mathematics)Pareto distributionWeibull modulusGeneralized Pareto distributionRatio distributionMoment-generating functionProbability density functionApplied mathematicsAsymptotic distributionMathematical analysisExtreme value theoryPhysicsEstimatorClassical mechanicsOpticsHydrology and Drought AnalysisStatistical Distribution Estimation and ApplicationsProbabilistic and Robust Engineering Design