Exponential Inverse Exponential (EIE) Distribution with Applications to Lifetime Data

Objective: This study aimed to extend and generalize the Inverse Exponential (IE) distribution by using the exponential generalized family of distributions. Materials and Methods: The compound distribution was studied while the expressions for its densities and basic statistical properties were derived and established. It was applied to three real life data and a simulation study was also conducted. Results: The shape of the Exponential Inverse Exponential (EIE) distribution is unimodal (or inverted bathtub) and its densities are more tractable than that of the Beta Inverse Exponential distribution. It was discovered that the EIE distribution has a better fit than the baseline distribution in two of the three applications but when the data set is over-dispersed, it failed to perform better. Conclusion: The EIE is an improvement over the IE distribution except for cases with outliers. The parameters of the EIE are stable and the mean square error reduces as the sample size increases.