Fitting Real Data Sets by a New Version of Gompertz Distribution

Abstract

The Poisson Inverted Shifted Gompertz distribution is a new type of distribution that comes from the Poisson-generating family of distributions and is based on the "inverted shifted Gompertz distribution." This distribution has significant statistical characteristics, with clear formulations obtained mathematically. We use three distinct approaches to estimate the parameters of the distribution: maximum likelihood estimation (MLE), least-squares estimation (LSE), and Cramer-Von-Mises estimation (CVME). We undertake a simulation experiment to thoroughly assess the efficacy of maximum likelihood estimation (MLE). Empirical data from engineering and medical fields demonstrate the relevance of our suggested model. We meticulously evaluate the goodness-of-fit of the Poisson Inverted Shifted Gompertz distribution using several statistical tests and graphical techniques. Our suggested distribution demonstrates enhanced fitting capabilities and more flexibility compared to many widely used lifespan distributions. Furthermore, we investigate the Bayesian viewpoint of the proposed model by using Hamiltonian Monte Carlo (HMC) simulation methods. This detailed study gives you a full picture of how the Poisson Inverted Shifted Gompertz distribution can be used in many different areas.