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Unit Exponential Probability Distribution: Characterization and Applications in Environmental and Engineering Data Modeling

Author

Listed:
  • Hassan S. Bakouch

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
    Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt)

  • Tassaddaq Hussain

    (Department of Statistics, Mirpur University of Science and Technology, Mirpur 10250, Pakistan)

  • Marina Tošić

    (Department of Mathematics, Faculty of Sciences & Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia)

  • Vladica S. Stojanović

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11060 Belgrade, Serbia)

  • Najla Qarmalah

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia)

Abstract

Distributions with bounded support show considerable sparsity over those with unbounded support, despite the fact that there are a number of real-world contexts where observations take values from a bounded range (proportions, percentages, and fractions are typical examples). For proportion modeling, a flexible family of two-parameter distribution functions associated with the exponential distribution is proposed here. The mathematical and statistical properties of the novel distribution are examined, including the quantiles, mode, moments, hazard rate function, and its characterization. The parameter estimation procedure using the maximum likelihood method is carried out, and applications to environmental and engineering data are also considered. To this end, various statistical tests are used, along with some other information criterion indicators to determine how well the model fits the data. The proposed model is found to be the most efficient plan in most cases for the datasets considered.

Suggested Citation

  • Hassan S. Bakouch & Tassaddaq Hussain & Marina Tošić & Vladica S. Stojanović & Najla Qarmalah, 2023. "Unit Exponential Probability Distribution: Characterization and Applications in Environmental and Engineering Data Modeling," Mathematics, MDPI, vol. 11(19), pages 1-22, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4207-:d:1255827
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    References listed on IDEAS

    as
    1. Mustafa Ç. Korkmaz & Zehra Sedef Korkmaz, 2023. "The unit log–log distribution: a new unit distribution with alternative quantile regression modeling and educational measurements applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 50(4), pages 889-908, March.
    2. M. Ahsanullah & M. E. Ghitany & D. K. Al-Mutairi, 2017. "Characterization of Lindley distribution by truncated moments," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(12), pages 6222-6227, June.
    3. Luiz R. Nakamura & Pedro H. R. Cerqueira & Thiago G. Ramires & Rodrigo R. Pescim & R. A. Rigby & Dimitrios M. Stasinopoulos, 2019. "A new continuous distribution on the unit interval applied to modelling the points ratio of football teams," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(3), pages 416-431, February.
    4. Sanku Dey & Josmar Mazucheli & M. Z. Anis, 2017. "Estimation of reliability of multicomponent stress–strength for a Kumaraswamy distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1560-1572, February.
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    Cited by:

    1. Vladica S. Stojanović & Tanja Jovanović Spasojević & Mihailo Jovanović, 2024. "Laplace-Logistic Unit Distribution with Application in Dynamic and Regression Analysis," Mathematics, MDPI, vol. 12(14), pages 1-21, July.
    2. Hua Xin & Yuhlong Lio & Ya-Yen Fan & Tzong-Ru Tsai, 2024. "Bias-Correction Methods for the Unit Exponential Distribution and Applications," Mathematics, MDPI, vol. 12(12), pages 1-17, June.

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