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.
Highlights
Clement Boateng Ampadu and Abdulzeid Yen AnafoStatistical distributions have been developed in recent years by researchers in order to model and predict real world data
We present the GA-G family of distributions and applies the proposed family of distributions to the Weibull distribution and this new distribution is named the generalized Ampadu-Weibull distribution (GA-W for short)
Where λ ∈ (− ∞, 0) ∪ (0, ∞), x ∈ R, ξ is a vector of parameters in the baseline distribution with cumulative distribution function (CDF) G and probability density function (PDF) g, and β > 0
Summary
Statistical distributions have been developed in recent years by researchers in order to model and predict real world data. In relation to [1], many lifetime distributions have been proposed Some these distributions include, Exponentiated Exponential in Gupta and Kundu [2], Exponentiated beta in Nadarajah [3], exponentiated lognormal in Shirke and Kakade [4], exponentiated Kumaraswamy in Lemonte et al [5], Exponentiated Power Lindley in Ashour and Eltehiwy [6] and exponentiated Weibull-Pareto in Afify et al [7]. Another prominent method in this area, is Marshall-Olkin family of distributions proposed by Marshall and Olkin [8] defined by the CDF, F
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
