Latest revision as of 12:36, 20 July 2026

Abstract

It is necessary to construct constrained families of probability distributions when dealing with data that is unit-limited by definition, such as rates, proportions, and probabilities. These models are widely used in fields such as ecology, epidemiology, reliability, and economics. To make sense of the complex real-world events, robust and adaptable statistical methods are required across all these fields. Unit power Shanker distribution (UPSD) is a novel bounded probability distribution that we introduce for this purpose. Key statistical properties, including the quantile function, reliability measures, moments, cumulative distribution function, and probability density function, are derived and studied in detail. Furthermore, the analytical links between the Tsallis entropy and other entropy measures, such as extropy, Shannon, Rényi, and Arimoto, are clarified. Maximum likelihood, Anderson-Darling, Cramér-von Mises, maximum product of spacings, least squares, and variants thereof are among the parameter estimation approaches that we examine. We assess the efficacy of several goodness-of-fit estimation methodologies for bias and mean squared error using a thorough Monte Carlo simulation study. The findings demonstrate that, in every case, the maximum likelihood estimation method outperforms the maximum product of spacings method. In various technical and scientific settings, the UPSD offers a robust and adaptable alternative for analyzing limited data.OPEN ACCESS Received: 07/04/2026 Accepted: 09/05/2026 Published: 21/07/2026

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