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AIMS Mathematics

2025, Volume 10, Issue 11: 25939-26057. doi: 10.3934/math.20251146
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Research article Special Issues

A review of unit continuous probability distributions

  • 1.
    Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia; emmanuel.afuecheta@kfupm.edu.sa
  • 2.
    Department of Mathematics, Khalifa University, P.O. Box 127788, Abu Dhabi, UAE; idika.okorie@ku.ac.ae
  • 3.
    Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia; g202110510@kfupm.edu.sa
  • 4.
    Department of Mathematics, University of Manchester, Manchester M13 9PL, UK; mbbsssn2@manchester.ac.uk
  • 5.
    Interdisciplinary Research Center for Finance and Digital Economy, KFUPM, Saudi Arabia; emmanuel.afuecheta@kfupm.edu.sa
  • Published: 11 November 2025

  • MSC : 62E99

  • Unit continuous probability distributions play a fundamental role in modeling variables bounded within the interval $ [0, 1] $, such as proportions and probabilities. In recent decades, there has been a significant increase in the development of new parametric families of these distributions. In this work, we present a comprehensive and up-to-date review of more than one hundred unit continuous distributions, including classical models, such as the beta and Kumaraswamy distributions, along with their various extensions. We examined key statistical properties such as moments and demonstrated the practical effectiveness of twelve selected distributions through applications to nine distinct datasets, thereby highlighting their flexibility in modeling a wide range of data types. To the best of our knowledge, this is the most extensive review focused specifically on unit distributions and is a valuable reference for researchers and practitioners.

    Citation: Emmanuel Afuecheta, Idika E. Okorie, Haady Jallow, Saralees Nadarajah. A review of unit continuous probability distributions[J]. AIMS Mathematics, 2025, 10(11): 25939-26057. doi: 10.3934/math.20251146

    Related Papers:

  • Unit continuous probability distributions play a fundamental role in modeling variables bounded within the interval $ [0, 1] $, such as proportions and probabilities. In recent decades, there has been a significant increase in the development of new parametric families of these distributions. In this work, we present a comprehensive and up-to-date review of more than one hundred unit continuous distributions, including classical models, such as the beta and Kumaraswamy distributions, along with their various extensions. We examined key statistical properties such as moments and demonstrated the practical effectiveness of twelve selected distributions through applications to nine distinct datasets, thereby highlighting their flexibility in modeling a wide range of data types. To the best of our knowledge, this is the most extensive review focused specifically on unit distributions and is a valuable reference for researchers and practitioners.



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