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Entropy
Volume 27
Issue 12
10.3390/e27121188
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Review

A Review: Construction of Statistical Distributions

by
Kai-Tai Fang
1,2,
Yu-Xuan Lin
1,3 and
Yu-Hui Deng
1,3,*
1
Faculty of Science and Technology, Beijing Normal-Hong Kong Baptist University, 2000 Jintong Road, Tangjiawan, Zhuhai 519087, China
2
The Key Lab of Random Complex Structures and Data Analysis, The Chinese Academy of Sciences, Beijing 100045, China
3
Guangdong 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
*
Author to whom correspondence should be addressed.
Entropy 2025, 27(12), 1188; https://doi.org/10.3390/e27121188 (registering DOI)
Submission received: 7 October 2025 / Revised: 6 November 2025 / Accepted: 20 November 2025 / Published: 23 November 2025
(This article belongs to the Special Issue Number Theoretic Methods in Statistics: Theory and Applications)
Review Reports Versions Notes

Abstract

Statistical modeling is fundamentally based on probability distributions, which can be discrete or continuous and univariate or multivariate. This review focuses on the methods used to construct these distributions, covering both traditional and newly developed approaches. We first examine classic distributions such as the normal, exponential, gamma, and beta for univariate data, and the multivariate normal, elliptical, and Dirichlet for multidimensional data. We then address how, in recent decades, the demand for more flexible modeling tools has led to the creation of complex meta-distributions built using copula theory.
Keywords: construction of statistical distribution; distribution family; entropy; function of random variables; mean square error; quasi-Monte Carlo; representative points; statistical distribution construction of statistical distribution; distribution family; entropy; function of random variables; mean square error; quasi-Monte Carlo; representative points; statistical distribution

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MDPI and ACS Style

Fang, K.-T.; Lin, Y.-X.; Deng, Y.-H. A Review: Construction of Statistical Distributions. Entropy 2025, 27, 1188. https://doi.org/10.3390/e27121188

AMA Style

Fang K-T, Lin Y-X, Deng Y-H. A Review: Construction of Statistical Distributions. Entropy. 2025; 27(12):1188. https://doi.org/10.3390/e27121188

Chicago/Turabian Style

Fang, Kai-Tai, Yu-Xuan Lin, and Yu-Hui Deng. 2025. "A Review: Construction of Statistical Distributions" Entropy 27, no. 12: 1188. https://doi.org/10.3390/e27121188

APA Style

Fang, K.-T., Lin, Y.-X., & Deng, Y.-H. (2025). A Review: Construction of Statistical Distributions. Entropy, 27(12), 1188. https://doi.org/10.3390/e27121188

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