The Length-Biased Gamma-Rayleigh Distribution with Applications

Abstract

In this study, we introduce a new class of length-biased distribution called the length-biased Gamma-Rayleigh (LBGR) distribution. Various mathematical properties, including its limit th behavior, the r moment, the moment generating function, the survival function, and the hazard ratio function, are derived. Maximum-likelihood estimation is used to estimate the parameters of the LBGR distribution. Three environmental datasets were used in a comparison of distributions to determine which one could best fit the data. The results indicate that the LBGR distribution provided a better fit than the Rayleigh, lognormal, gamma, and gamma-Rayleigh distributions.