The Length-Biased Gamma-Rayleigh Distribution with Applications

Authors

  • Tanachot Chaito Ph.D. Program in Applied Statistics, Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand
  • Pimwarat Nanthaprut Data Science Research Centre, Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand
  • Nawapon Nakharutai Data Science Research Centre, Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand.
  • Manad Khamkong Data Science Research Centre, Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand

Keywords:

Average wind speed, fit distribution, maximum likelihood estimation, model selection criteria, positively skewness

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 behavior, the rth 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.

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Published

2022-03-28

Issue

Section

Articles