Model and Properties of Cauchy Modified Inverse Gompertz Distribution with Application to a Real Data Set

Abstract

In this study, we introduce the Cauchy modified inverse Gompertz distribution as a new probability model. Utilizing the modified inverse Gompertz distribution as its baseline distribution, this model blends the Cauchy family of distributions. Our aim is to utilize this model for lifetime data analysis. We have inferred formulas for some basic properties of the model. We have also included graphic representations of the hazard rate and probability density curves. We observed that the probability density function displays positive skewness, while the hazard rate function plot shows an increasing-decreasing pattern. We used the Cramer-Von Mises method, the least squares approach, and maximum likelihood estimation to estimate the model parameters. We employed several statistical criteria to validate our model, including the corrected Akaike’s, the Bayesian, the Hannan-Quinn, as well as Akaike’s information criterion. We also utilized Q-Q and P-P graphs for further confirmation. To assess goodness of fit, we used the Kolmogorov-Smirnov, Anderson-Darlin, and Cramer-von Mises tests. The empirical results of the study show that it gives a better fit to the real data set. All numerical computations were conducted using the R programming language.