# The Generalized Ampadu-G Family of Distributions: Properties, Applications and Characterizations

• Clement Boateng Ampadu 31 Carrolton Road, Boston, MA 02132-6303, USA
• Abdulzeid Yen Anafo University of Mines and Technology, P.O. Box 237, Tarkwa, Ghana, West Africa
Keywords: Ampadu-G, Weibull distribution, Poisson distribution, survival function, hazard rate function, statistical properties, characterization theorem, simulation

### Abstract

This paper introduces a new class of distributions called the generalized Ampadu-G (GA-G for short) family of distributions, and with a certain restriction on the parameter space, the family is shown to be a life-time distribution. The shape of the density function and hazard rate function of the GA-G family is described analytically. When G follows the Weibull distribution, the generalized Ampadu-Weibull (GA-W for short) is presented along with its hazard and survival function. Several sub-models of the GA-W family are presented. The transformation technique is applied to this new family of distributions, and we obtain the quantile function of the new family. Power series representations for the cumulative distribution function (CDF) and probability density function (PDF) are also obtained. The rth non-central moments, moment generating function, and Renyi entropy associated with the new family of distributions are derived. Characterization theorems based on two truncated moments and conditional expectation are also presented. A simulation study is also conducted, and we find that using the method of maximum likelihood to estimate model parameters is adequate. The GA-W family of distributions is shown to be practically significant in modeling real life data, and is shown to be superior to some non-trivial generalizations of the Weibull distribution. A further development concludes the paper.

Published
2020-05-20
How to Cite
Ampadu, C. B., & Anafo, A. Y. (2020). The Generalized Ampadu-G Family of Distributions: Properties, Applications and Characterizations . Earthline Journal of Mathematical Sciences, 4(1), 139-167. https://doi.org/10.34198/ejms.4120.139167
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Articles