Weighted Rayleigh Distribution

Adetunji K. Ilori, Omaku P. Enesi, Kole Emmanuel, Dayo V. Kayode and Adebisi Michael
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Adetunji K. Ilori: Statistics Programme, National Mathematical Center, Kaduna-Lokoja Expressway, Sheda, Kwali Abuja, Nigeria
Omaku P. Enesi: Department of Mathematics and Statistics, Federal Polytechnic, Nassarawa
Kole Emmanuel: Department of Mathematics and Statistics, Kaduna Polytechnic, Kaduna
Dayo V. Kayode: Department of Statistics, University of Abuja, FCT, Nigeria
Adebisi Michael: Nigeria Centre for Disease Control and Prevention

International Journal of Research and Innovation in Applied Science, 2024, vol. 9, issue 8, 323-336

Abstract: This paper introduces the Weighted Rayleigh (WR) distribution by inducing inverted weight function into the existing Rayleigh distribution. Statistical and mathematical expressions of its properties such as Survival Function, Hazard Function, Moments, Moment Generating Function, Mean Deviation and Renyi entropy were explicitly derived. The model’s parameter was estimated using maximum likelihood method of estimation. Two real life data sets on cancer and waiting time before service were considered to assess the flexibility of the Weighted Rayleigh distribution over existing distributions. The distributions performance were compared using Log-likelihood and Akaike Information Criteria (AIC). The Weighted Rayleigh distribution fits the real life data better than the Rayleigh, Inverse Weibull (IW) and Weighted Inverse Weibull (WIW) distributions.

Date: 2024
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