Generalized Kumaraswamy Generalized Power Gompertz Distribution: Statistical Properties, Application, and Validation Using a Modified Chi-Squared Goodness of Fit Test

Abstract

A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function and cumulative distribution function is presented. The statistical features of the Generalized Kumaraswamy Generalized Power Gompertz distribution are systematically derived and adequately studied. The estimation of the model parameters in the absence of censoring and under-right censoring is performed using the method of maximum likelihood. The test statistic for rightcensored data, criteria test for GKGPG distribution, estimated matrix Ŵ , Ĉ , and Ĝ , criteria test 2 n Y , alongside the quadratic form of the test statistic is derived. Mean simulated values of maximum likelihood estimates γ̂ and their corresponding square mean errors are presented and confirmed to agree closely with the true parameter values. Simulated levels of significance for ( ) 2 n Y γ test for the GKGPG model against their theoretical values were recorded. We conclude that the null hypothesis for which simulated samples are fitted by GKGPG distribution is widely validated for the different levels of significance considered. From the summary of the results of the strength of a specific type of braided cord dataset on the GKGPG model, it is observed that the proposed GKGPG model fits the data set for a significance level ε = 0.05. How to cite this paper: Maxwell, O., Onyedikachi, I.P., Aidi, K., Akpa, C.I. and SeddikAmeur, N. (2022) Generalized Kumaraswamy Generalized Power Gompertz Distribution: Statistical Properties, Application, and Validation Using a Modified Chi-Squared Goodness of Fit Test. Applied Mathematics, 13, 243-262. https://doi.org/10.4236/am.2022.133019 Received: January 22, 2022 Accepted: March 15, 2022 Published: March 18, 2022 Copyright © 2022 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access