A novel inverse statistical distribution: theoretical development with applications to reliability and environmental data

Abstract Modeling real-world data is important in engineering, finance, environmental science, and medical science. Probability distributions are widely used to model such data. However, no single distribution can adequately fit all types of data, which creates a need for flexible distributions. In this study, a new extension of the Chris Jerry distribution (CJD), called the inverse Chris Jerry distribution (ICJD), is introduced using the inverse transformation technique. The probability density function of the ICJD can take right-skewed, reverse J, and inverted bathtub shapes. Its hazard rate function can also take upside-down and decreasing shapes. Several properties of the ICJD are derived, including the mode, harmonic mean, moments, inverse moments, conditional moments, incomplete moments, and order statistics. The model parameter is estimated using 15 estimation methods, and a simulation study is carried out to compare their performance. The simulation results show that the estimators perform consistently as the sample size increases, with the maximum likelihood method performing best. The modeling ability of the ICJD is demonstrated using two real datasets from environmental science and reliability engineering. The results show that the ICJD provides a better fit than the existing inverted distributions considered for both datasets, demonstrating its usefulness in modeling annual flood discharge rates and repair times of an airborne communication transceiver.