article · Axioms
A new statistical model called the unit-power Burr X distribution provides a way to analyse bounded data restricted to the unit interval. Derived from an inverse exponential transformation of the power Burr X distribution, its mathematical properties include moments, quantile functions, stochastic ordering, stress-strength reliability, and several entropy measures of uncertainty. Parameter estimation is handled through a Bayesian framework employing both symmetric and asymmetric loss functions, with credible intervals built from marginal posterior distributions. Monte Carlo simulations demonstrate the accuracy of these estimators across varied metrics. When tested against existing alternative distributions, the model shows superior fit when analysing real-world COVID-19 datasets from Saudi Arabia and the United Kingdom, indicating its effectiveness in capturing bounded epidemiological trends.
Many datasets in healthcare, engineering, and the physical sciences are constrained between zero and one, such as rates, proportions, or probabilities. Developing precise statistical distributions for bounded intervals enables more accurate risk assessments and uncertainty quantification. Applying these methods to epidemic metrics helps researchers and analysts better describe patterns in disease progression, potentially guiding clearer insights from complex public health data.
The research presents early-stage theoretical and computational tools that could assist data scientists and biostatistical software developers. By improving the modelling of rates and bounded metrics, the distribution could be integrated into analytical packages used for epidemiological surveillance or reliability engineering. However, the work currently exists at the stage of foundational mathematical modelling and exploratory data fitting, requiring implementation into commercial statistical software before widespread industry adoption.
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The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model’s parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom.
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DOI: 10.3390/axioms12030297
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