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The generalized Cauchy family of distributions with applications

Author

Listed:
  • Ayman Alzaatreh

    (Nazarbayev University)

  • Carl Lee

    (Central Michigan University)

  • Felix Famoye

    (Central Michigan University)

  • Indranil Ghosh

    (University of North Carolina Wilmington)

Abstract

A family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value, and Fréchet distributions. Several general properties of the T-Cauchy{Y} family are studied in detail including moments, mean deviations and Shannon’s entropy. Some members of the T-Cauchy{Y} family are developed and one member, gamma-Cauchy{exponential} distribution, is studied in detail. The distributions in the T-Cauchy{Y} family are very flexible due to their various shapes. The distributions can be symmetric, skewed to the right or skewed to the left.

Suggested Citation

  • Ayman Alzaatreh & Carl Lee & Felix Famoye & Indranil Ghosh, 2016. "The generalized Cauchy family of distributions with applications," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    • Handle: RePEc:spr:jstada:v:3:y:2016:i:1:d:10.1186_s40488-016-0050-3
    DOI: 10.1186/s40488-016-0050-3
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    References listed on IDEAS

    as
    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    2. Jese Maria Sarabia & Enrique Castillo, 2005. "About a class of max-stable families with applications to income distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 505-527.
    3. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
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    Cited by:

    1. Muhammad Ijaz & Syed Muhammad Asim & Alamgir & Muhammad Farooq & Sajjad Ahmad Khan & Sadaf Manzoor, 2020. "A Gull Alpha Power Weibull distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    2. Muhammad Ijaz & Wali Khan Mashwani & Samir Brahim Belhaouari, 2020. "A novel family of lifetime distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-15, October.

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