UNIT PROBABILITY DISTRIBUTIONS: A COMPREHENSIVE REVIEW OF MODELS, PROPERTIES, AND APPLICATIONS

Authors

  • Sule Omeiza Bashiru
    Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
  • Alhaji Modu Isa
    Department of Mathematics and Computer Science, Borno State University, Maiduguri, Nigeria
  • Ibrahim Ali
    Department of Mathematics and Computer Science, Borno State University, Maiduguri, Nigeria
  • Kingsley Chinedu Arum
    Department of Statistics, University of Nigeria, Nsukka, Nigeria.
  • Henrietta Ebele Oranye
    Department of Statistics, University of Nigeria, Nsukka, Nigeria.
  • Tobias Ejiofor Ugah
    Department of Statistics, University of Nigeria, Nsukka, Nigeria.
  • Nkechi Grace Okoacha
    Basic Science Unit, School of Science and Technology, Pan-Atlantic University, Nigeria. Lagos, Nigeria.

Keywords:

Unit probability distributions, Bounded data, Transformation techniques, Flexible models, Parameter estimation, Real-world applications

Abstract

Unit probability distributions defined on the standard interval (0, 1) serve as foundational tools for modeling data constrained within this bounded domain. Such data frequently emerge in disciplines where proportions, rates, and probabilities are analyzed, including economics, finance, hydrology, environmental sciences, biomedical research, and reliability engineering. Traditional models such as the Beta and Kumaraswamy distributions have long provided flexible frameworks for these applications. However, the increasing complexity of real-world phenomena has spurred the development of more versatile and specialized unit distributions. This article presents a comprehensive review of the literature on unit probability distributions, encompassing both classical models and recent innovations. Emphasis is placed on transformation techniques used to generate new families, key analytical properties, and a comparative evaluation of estimation methods. A diverse array of real-world applications is examined, highlighting the practical relevance and empirical performance of modern unit distributions across multiple domains. By synthesizing these developments, the review offers a structured resource to support further methodological advancement and informed model selection for bounded data analysis.

Dimensions

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Published

15-07-2025

How to Cite

UNIT PROBABILITY DISTRIBUTIONS: A COMPREHENSIVE REVIEW OF MODELS, PROPERTIES, AND APPLICATIONS. (2025). FUDMA JOURNAL OF SCIENCES, 9(7), 126-132. https://doi.org/10.33003/fjs-2025-0907-3699

Issue

Vol. 9 No. 7 (2025): FUDMA Journal of Sciences - Vol. 9 No. 7

Section

Review Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

UNIT PROBABILITY DISTRIBUTIONS: A COMPREHENSIVE REVIEW OF MODELS, PROPERTIES, AND APPLICATIONS. (2025). FUDMA JOURNAL OF SCIENCES, 9(7), 126-132. https://doi.org/10.33003/fjs-2025-0907-3699

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