Class of Generalized Power Function Distributions: Properties and Applications

There are different frameworks available in theory used in developing convoluted distributions. One of the unique frameworks is the T-R{Y} framework. The T-R{Y} framework is used to generate distributions that have more than one mode, and the developed distributions are weighted hazard function of the base line distributions. The two parameter Power function distribution is a useful distribution that has the properties of Pareto, Weibull, Uniform, Kumaraswamy, and Beta distributions. The combination of gamma and power functions distributions with both having shape parameters and the upper bound parameter of power function distribution will produce a distribution, which is more flexible than gamma and power function distributions. The new distribution will present new opportunities for assessing reliability and survival data in different field of study. This research however, developed and studied the properties of T-Power{Y} family of distributions using the T-R{Y} framework. A special case of this family was developed as the Gamma-Power {log-logistic} distribution (GPLD), and was characterized using different functions and different properties of the distribution were derived. We used Maximum Likelihood Estimation (MLE) method to estimate the distribution parameters, except for that of the upper bound. Simulation study was carried out to test the consistency of the parameters estimates and was applied to two real life data. The results of the new distribution were compared with existing distributions, and the comparison shows that the proposed GPLD performed best when compared with some existing distributions.

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