An Improved Extension of Unit Moment Exponential Distribution: Mathematics, Inference, and Applications

This study contributes to the derivation of a bounded probability model for unit interval data analysis. The proposed model is named the Sine Unit Moment Exponential (SUME) distribution. This SUME model has the potential to model both the monotone increase and the bathtub shape for the hazard function. We investigate various statistical properties, including mixture representation, moments, quantile function, mean residual life function, and order statistics. The parameter estimation of the SUME distribution is discussed using six different estimation approaches. A comprehensive simulation study is performed to assess frequentist properties of the considered estimation methodologies. Two different datasets related to failure time and milk production are utilized to evaluate the practicality and flexibility of the proposed distribution over renowned unit interval distributions.