Statistical properties and different estimation methods of Inverse Unit Gompertz Distribution with applications on health data sets

Abstract

Continuous probability distributions are always helpful in lifetime data and health-related data sets. Various techniques exist to develop new probability distributions, adding new parameters and applying different transformations. Adding new parameters is not always good; rather, it can also have complex expressions for the function and properties. This research aimed to develop a model without adding new parameters, which will work more efficiently than the existing models. This study proposes a new probability density function by taking the inversion of a random variable whose probability density function is Unit Gompertz Distribution. The newly proposed distribution is called an Inverse Unit Gompertz Distribution (IUGD). Various properties include reliability/survivorship measures, odd function, elasticity, and Mills ratio. Different statistical properties such as moments, quantile function, and Lorenz and Bonferroni curves for IUGD are developed. Five estimation methods are discussed for unknown parameters of the IUGD, and simulations have been conducted. Finally, IUGD is applied to two real-life data sets, i.e., COVID-19 death rates in the Netherlands and the pain relief time of individuals who received analgesics experienced. IUGD is flexible compared to other competing densities. Moreover, the proposed density can be used for health-related data sets to take accurate precautions and treatments.