Statistical analysis of radiation data using power unit moment exponential distribution

This article introduces the Power unit moment exponential (PUME) distribution, a novel lifetime model designed explicitly for data confined to the interval [0,1]. The statistical properties of the PUME distribution are comprehensively analyzed, including moments, inverse moments, variance, skewness, kurtosis, hazard rate function, quantile function, Bonferroni and Lorenz curves, and the Rényi entropy measure. Various estimation techniques, such as maximum likelihood, least squares, weighted least squares, maximum product of spacings, Cramér-von Mises, Anderson-Darling, and right-tail Anderson-Darling methods, are explored. The model's applicability and performance are demonstrated through a simulation study and its application to two radiation datasets. Comparative analyses reveal that the PUME distribution outperforms existing models, underscoring its utility and effectiveness in modeling lifetime radiation data.