Abstract

This paper proposes a new Holistic and Generalized Continuous Semibounded distribution which is also called as H-G family of Semi-bounded distribution. The density function of the proposed distribution is expressed in terms of Kummer’s U function. The cumulative distribution function and the constants such as Central moments, Non-central moments, Skewness, kurtosis, Shannon’s differential entropy are also computed. Moreover, the generating functions such as moment, Cumulant, Characteristic, Survival, hazard and Cumulative functions are also derived. The special cases of the H-G family are visualized by shifting the location, scale and shape parameters, two broad and generalized families namely Amoroso (or) Gamma and Beta Prime family of distributions are shown. Under these two families, 56 distributions include Generalized scaled and generalized families of Semi-bounded are exhibited by the authors. Almost all the families of Semi-bounded distributions are special cases of the proposed H-G family and we also discussed the estimation of parameters by the method of unconstrained and constrained maximum likelihood approach by using Nonlinear Programming with some applications. Finally, the motivation of the paper is to provide a single distribution which is holistic and generalized nature, in which a semi-bounded random variable has the entirety through the H-G family of distribution.

Author: G. S. David Sam Jayakumar, A. Sulthan and W. Samuel

Received on: August, 2019

Accepted on: August, 2020