Transmuted Unit Moment Exponential Distribution: A Flexible Model to Analyze Kidney Dialysis and Arthritic Relief Data

Abstract

In this paper, we introduce a new unit interval probability model, called the transmuted unit moment exponential (TUME) distribution, to provide a flexible framework for modeling bounded data arising in reliability and lifetime analysis. The TUME model extends the baseline unit moment exponential distribution by incorporating a transmutation parameter, which significantly enhances its ability to capture varying shapes, including different levels of skewness and tail behavior. We derive several important statistical properties of the new distribution, including closed-form expressions for the moments, moment generating function, incomplete moments, mean residual life function, stochastic ordering, order statistics, and entropy. Parameter estimation is performed using the maximum likelihood method, and the finite-sample performance of the estimators is evaluated through an extensive Monte Carlo simulation study based on bias, mean relative error, and mean squared error. The results demonstrate that the proposed model provides greater flexibility than the baseline distribution, with improved capability to accommodate diverse data patterns on the unit interval. Applications to real-life datasets show that the TUME distribution yields a better fit compared to existing competing models, as supported by standard goodness-of-fit criteria. These findings highlight the usefulness of the TUME model as an effective alternative for analyzing bounded lifetime data.