Modeling extreme events and waiting-time phenomena: an inverse log-shifted Gompertz statistical model for physical, environmental, and biomedical data

Abstract

Statistical modeling of real-life data from hydrology, engineering, and medical sciences often requires flexible probability distributions that can capture skewness, heavy tails, and complex hazard rate patterns. Classical distributions often do not provide an adequate fit to such data because of their limited flexibility. A new probability model called the inverse log-shifted Gompertz distribution is proposed in this study by applying the inverse scheme to the log-shifted Gompertz distribution. Several statistical and reliability properties of the model are derived. The estimation of the parameters is carried out using fifteen different estimation methods, and a simulation study is conducted to assess the finite-sample performance of the estimators. Three real datasets involving annual maximum flood discharges, mechanical component failure times, and analgesic relief times are used to demonstrate the practical performance of the proposed model. Standard goodness-of-fit measures, such as the Akaike information criterion, Hannan–Quinn information criterion, root mean square error, Kolmogorov–Smirnov statistic with its p-value, and Anderson–Darling statistic with its p-value, are used to compare the models. The results show that the proposed distribution provides a better fit than several classical distributions, which demonstrates its usefulness in modeling complex data.