Analytical Properties of the Uniform Exponential Distribution - Ayenigba, Alfred Ayo; Ogunkoya, C. O. (Darul Yasin Al Sys, 2025)
This study introduces a new probability distribution, the Uniform–Exponential Distribution, constructed by combining the Uniform and Exponential distributions to capture phenomena characterized by both constant and exponentially decaying behavior. The distribution is developed within the T-X family framework, and its fundamental properties are derived, including the probability density function (PDF), cumulative distribution function (CDF), hazard function, reverse hazard function, and moment-generating function (MGF). Analytical expressions for key moments—mean, variance, skewness, and kurtosis—are presented to describe the distribution’s shape and behavior. Parameter estimation is conducted using maximum likelihood estimation (MLE), ensuring statistical rigor in model fitting. Theoretical examples are provided to illustrate the distribution’s practical relevance. Potential applications are identified in reliability analysis, survival modeling, and environmental science, underscoring the distribution’s flexibility and utility in modeling diverse real-world processes.