Simulation and Application of the Transmuted Unit Burr XII Distribution in Real-World Data Analysis

This paper introduces the Transmuted Unit Burr XII (TrUBXII) distribution, a flexible probability model for analyzing bounded data that exhibit skewness and heavy-tailed characteristics. The proposed distribution is derived by incorporating a transmutation parameter into the unit-support Burr XII framework, extending existing bounded distributions and enhancing modeling flexibility for data on the interval (0, 1). Several fundamental statistical properties of the distribution are derived, including its moments, quantile function, and hazard rate function, which provide insight into its structural features. Parameter estimation is conducted using the maximum likelihood approach, and the finite-sample behavior of the estimators is examined through an extensive Monte Carlo simulation study with improved design and performance evaluation metrics. The practical relevance of the TrUBXII distribution is illustrated through an application to a real dataset of residence times under three watering regimes (clean air, high-watered, and low-watered plants), which exhibits the asymmetry and boundary accumulation that motivate the proposed model. Comparative analyses with established bounded distributions, including the Beta and Kumaraswamy models, indicate that the TrUBXII distribution provides a superior fit, particularly for datasets characterized by asymmetry and extreme observations. Therefore, the proposed model offers a robust and versatile framework for bounded data analysis, supported by reproducible implementation in the R programming environment.