A New Untied Prakaamy Distribution: Properties and Application

This study introduces the Unit Prakaamy Distribution (UPD), a bounded version of the Prakaamy distribution,and examines its statistical and reliability properties. The theoretical properties of the UPD include mean, variance, skewness, kurtosis, non-central moments, Bonferroni and Lorenz curves, as well as the survival and hazard functions. Measures of uncertainty, such as Shannon and R´enyi entropy, are also considered. Parameter estimation is performed using Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE),Weighted Least Squares Estimation (WLS), and the Cram´er–von Mises (CvM) method, with Monte Carlo simulations showing that MLE consistently provides the most accurate estimates in terms of bias and mean squared error. The applicability of the UPD is further demonstrated through real-world datasets, where it outperforms competing models, highlighting its flexibility and robustness for modeling data constrained to the unit interval.