A CLASS OF POWER FUNCTION DISTRIBUTIONS: ITSPROPERTIES AND APPLICATIONS

Abstract

The T-R{Y} framework is a method of generating convoluted
probability distributions; which has generalized most of the existing methods. In the T-R{Y} framework, three independent distributions, T, R, and Y are combined to form a new distribution, X, where R is the baseline distribution.
The new distribution X is a weighted hazard function of the baseline distribution, R. Some distributions like Normal, Weibull, Uniform, Cauchy, and Gamma have been used as baseline distributions. However, the Power function distribution, despite its flexibility and simplicity of its functional form, has not been used as a baseline distribution in the T-R{Y} framework. In this work, we developed the T-Power function{Y} family of distributions using the T-R{Y} framework. We generated twelve convoluted distributions from the family developed, and derived the properties of Gamma-Power function{Log-logistic} distribution (GPLD) as a special case. The maximum likelihood estimation (MLE) method is used to estimate the parameters of the proposed distribution. A simulation study and application to two real-life datasets were carried out. The application results shows that the new GPLD perform favourable.