Simulation and Application of the Transmuted Unit Burr XII Distribution in Real-World Data Analysis
6 affiliations
- 1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
- 2Department of Statistics, Aliko Dangote University of Science and Technology, Wudil 713281, Kano, Nigeria
- 3Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil 713281, Kano, Nigeria
- 4Department of Statistics, University of Kashmir, Srinagar 190006, India
- 5Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23890, Saudi Arabia
- 6Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
Abstract
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.
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BibTeX
@article{alghamdi2026simulation,
title = {{Simulation and Application of the Transmuted Unit Burr XII Distribution in Real-World Data Analysis}},
author = {Fatimah M. Alghamdi and Abdulhameed Ado Osi and Muftahu Zubairu Ringim and Aadil Ahmad Mir and Souha K. Badr and Rana Bakoban and Gamal A. Abd-Elmougod},
journal = {Axioms},
year = {2026},
month = oct,
doi = {10.3390/axioms15100784},
url = {https://www.mdpi.com/2075-1680/15/10/784},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Simulation and Application of the Transmuted Unit Burr XII Distribution in Real-World Data Analysis
AU - Fatimah M. Alghamdi
AU - Abdulhameed Ado Osi
AU - Muftahu Zubairu Ringim
AU - Aadil Ahmad Mir
AU - Souha K. Badr
AU - Rana Bakoban
AU - Gamal A. Abd-Elmougod
PY - 2026
DA - 2026/10/19
JO - Axioms
DO - 10.3390/axioms15100784
UR - https://www.mdpi.com/2075-1680/15/10/784
AB - 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.
SN - 2075-1680
ER -