Revision as of 11:56, 20 July 2026

Abstract

The formulation of constrained families of probability distributions is crucial for analyzing data inherently limited to the unit interval, such as proportions, rates, and probabilities. These models have extensive applications across various domains, such as epidemiology, dependability, finance, and environmental research, where adaptable and resilient statistical instruments are essential for accurately representing intricate real-world phenomena. Motivated by this, our work presents the bounded Uma distribution (BUmD), an innovative probability model obtained by transforming the Uma distribution to the unit interval (0, 1). The suggested distribution maintains the flexibility of the Uma family while broadening its applicability to data represented as proportions, probabilities, and rates. We examine the essential statistical characteristics of the BUmD, encompassing its moments, quantile function, extropy, and reliability metrics, with a focus on its capacity to represent various hazard rate behaviors. Sixteen traditional and contemporary estimation techniques are employed to estimate the model parameters, and their efficacy is assessed through comprehensive Monte Carlo simulations using criteria such as bias, mean squared error, and goodness-of-fit measures. The simulation findings indicate that the maximum likelihood and maximum product of spacings estimators are the most efficient. The practical relevance of the BUmD is evidenced by its application to epidemiological and public health datasets, where it demonstrates enhanced flexibility and fitting performance relative to conventional models. The suggested distribution provides a robust and flexible tool for modeling bounded lifetime, reliability, and proportional data in the applied sciences.OPEN ACCESS Received: 07/04/2026 Accepted: 20/05/2026 Published: 21/07/2026

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