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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.<\/jats:p>","DOI":"10.3390\/e27121188","type":"journal-article","created":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T09:02:07Z","timestamp":1763974927000},"page":"1188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Review: Construction of Statistical Distributions"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5651-5156","authenticated-orcid":false,"given":"Kai-Tai","family":"Fang","sequence":"first","affiliation":[{"name":"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"},{"name":"The Key Lab of Random Complex Structures and Data Analysis, The Chinese Academy of Sciences, Beijing 100045, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1295-8094","authenticated-orcid":false,"given":"Yu-Xuan","family":"Lin","sequence":"additional","affiliation":[{"name":"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"},{"name":"Faculty of Science and Technology, Beijing Normal-Hong Kong Baptist University, 2000 Jintong Road, Tangjiawan, Zhuhai 519087, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu-Hui","family":"Deng","sequence":"additional","affiliation":[{"name":"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"},{"name":"Faculty of Science and Technology, Beijing Normal-Hong Kong Baptist University, 2000 Jintong Road, Tangjiawan, Zhuhai 519087, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,23]]},"reference":[{"key":"ref_1","unstructured":"Johnson, N.L., Kotz, S., and Balakrishnan, N. 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