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A Review: Construction of Statistical Distributions
Kai-Tai Fang1,2, Yu-Xuan Lin1,3, Yu-Hui Deng1,3
1Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science (IRADS), Beijing Normal-Hong Kong Baptist University, 2000 Jintong Road, Tangjiawan, Zhuhai 519087, China.
Entropy (Basel, Switzerland)
|December 24, 2025
Summary
This review explores methods for constructing probability distributions, covering traditional and advanced techniques. It highlights how copula theory enables complex meta-distributions for flexible statistical modeling.
Area of Science:
- Statistics
- Probability Theory
Background:
- Statistical modeling relies heavily on probability distributions.
- Distributions can be discrete or continuous, and univariate or multivariate.
Purpose of the Study:
- To review methods for constructing probability distributions.
- To cover both traditional and newly developed approaches.
- To discuss the role of copula theory in creating meta-distributions.
Main Methods:
- Examination of classic univariate distributions (normal, exponential, gamma, beta).
- Review of classic multivariate distributions (multivariate normal, elliptical, Dirichlet).
- Discussion of meta-distributions constructed using copula theory.
Main Results:
- Traditional distributions provide foundational tools for statistical analysis.
- Copula theory offers advanced methods for constructing complex, flexible distributions.
- Meta-distributions address the need for enhanced modeling capabilities.
Conclusions:
- A comprehensive understanding of distribution construction is crucial for statistical modeling.
- Advancements in methods, particularly copula theory, expand modeling flexibility.
- The review provides insights into both established and emerging distribution construction techniques.
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