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The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval

Author

Listed:
  • M. E. Ghitany
  • J. Mazucheli
  • A. F. B. Menezes
  • F. Alqallaf

Abstract

A new two-parameter distribution over the unit interval, called the Unit-Inverse Gaussian distribution, is introduced and studied in detail. The proposed distribution shares many properties with other known distributions on the unit interval, such as Beta, Johnson SB, Unit-Gamma, and Kumaraswamy distributions. Estimation of the parameters of the proposed distribution are obtained by transforming the data to the inverse Gaussian distribution. Unlike most distributions on the unit interval, the maximum likelihood or method of moments estimators of the parameters of the proposed distribution are expressed in simple closed forms which do not need iterative methods to compute. Application of the proposed distribution to a real data set shows better fit than many known two-parameter distributions on the unit interval.

Suggested Citation

  • M. E. Ghitany & J. Mazucheli & A. F. B. Menezes & F. Alqallaf, 2019. "The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(14), pages 3423-3438, July.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:14:p:3423-3438
    DOI: 10.1080/03610926.2018.1476717
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    Citations

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    Cited by:

    1. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Muhammad H. Tahir & Aqib Ali & Muhammad Zubair & Sania Anam, 2020. "Some New Facts about the Unit-Rayleigh Distribution with Applications," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    2. Muhammad Ahsan ul Haq & Sharqa Hashmi & Khaoula Aidi & Pedro Luiz Ramos & Francisco Louzada, 2023. "Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test," Annals of Data Science, Springer, vol. 10(2), pages 415-440, April.
    3. Liang Wang & Sanku Dey & Yogesh Mani Tripathi, 2022. "Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    4. Mohammed K. Shakhatreh & Mohammad A. Aljarrah, 2023. "Bayesian Analysis of Unit Log-Logistic Distribution Using Non-Informative Priors," Mathematics, MDPI, vol. 11(24), pages 1-18, December.

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