Poisson Inverted Shifted Gompertz Distribution with Applications to Engineering and Medical Data

A novel distribution is introduced herein, termed the "Poisson Inverted Shifted Gompertz Distribution," achieved by employing the Poisson-Generating family of distributions with the inverted shifted Gompertz distribution as its base. This distribution exhibits notable statistical properties, with explicit expressions derived for its survival function, hazard rate function, average residual life function, moments, quantile function, entropy, order statistics, skewness, and kurtosis. To estimate the distribution's parameters, we employ three different methods: Maximum Likelihood Estimation (MLE), Least-Square Estimation (LSE), and Cramer-Von-Mises Estimation (CVME). To comprehensively evaluate the performance of MLE, a simulation experiment is conducted. Furthermore, the applicability of our proposed model is demonstrated using real-world data from both engineering and medical domains. The goodness-of-fit of the Poisson Inverted Shifted Gompertz distribution is rigorously examined through various statistical tests and graphical methods. Compared to a selection of commonly used lifetime distributions, our proposed distribution exhibits superior fitting capabilities and greater flexibility. In addition, we explore the Bayesian perspective of the proposed model by employing Hamiltonian Monte Carlo (HMC) simulation techniques. This comprehensive analysis provides a holistic understanding of the Poisson Inverted Shifted Gompertz distribution's potential and applicability in various fields. Mathematical Subject Classification 2020: 62F10, 62F40, 62E10, 62E15