Open AccessA Study of Some Properties and Goodness-of-Fit of a Gompertz-Rayleigh Model
Author(s) -
Fadimatu Bawuro Mohammed,
Kabiru Ahmed Manju,
Umma Abdullahi,
Makama Musa Sani,
Samson Kuje
Publication year - 2020
Publication title -
asian journal of probability and statistics
Language(s) - English
Resource type - Journals
ISSN - 2582-0230
DOI - 10.9734/ajpas/2020/v9i230223
Subject(s) - rayleigh distribution , goodness of fit , gompertz function , rayleigh scattering , statistics , mathematics , range (aeronautics) , distribution (mathematics) , probability distribution , statistical physics , computer science , probability density function , mathematical analysis , engineering , physics , optics , aerospace engineering
The Rayleigh was obtained from the amplitude of sound resulting from many important sources by Rayleigh. It is continuous probability distribution with a wide range of applications such as in life testing experiments, reliability analysis, applied statistics and clinical studies. However, it is not flexible enough for modeling heavily skewed datasets as compared to compound distributions. In this paper, we introduce a new extension of the Rayleigh distribution by using a Gompertz-G family of distributions. This paper defines and studies a three-parameter distribution called “Gompertz-Rayleigh distribution”. Some properties of the proposed distribution are derived and discussed comprehensively in this paper and the three parameters are estimated using the method of maximum likelihood estimation. The goodness-of-fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real life data.