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A New Family of Generalized Distributions Based on Alpha Power Transformation with Application to Cancer Data

Author

Listed:
  • M. Nassar

    (Zagazig University)

  • A. Alzaatreh

    (American University of Sharjah)

  • O. Abo-Kasem

    (Zagazig University)

  • M. Mead

    (Zagazig University)

  • M. Mansoor

    (The Islamia University of Bahawalpur)

Abstract

In this paper, we propose a new method for generating distributions based on the idea of alpha power transformation introduced by Mahdavi and Kundu (Commun Stat Theory Methods 46(13):6543–6557, 2017). The new method can be applied to any distribution by inverting its quantile function as a function of alpha power transformation. We apply the proposed method to the Weibull distribution to obtain a three-parameter alpha power within Weibull quantile function. The new distribution possesses a very flexible density and hazard rate function shapes which are very useful in cancer research. The hazard rate function can be increasing, decreasing, bathtub or upside down bathtub shapes. We derive some general properties of the proposed distribution including moments, moment generating function, quantile and Shannon entropy. The maximum likelihood estimation method is used to estimate the parameters. We illustrate the applicability of the proposed distribution to complete and censored cancer data sets.

Suggested Citation

  • M. Nassar & A. Alzaatreh & O. Abo-Kasem & M. Mead & M. Mansoor, 2018. "A New Family of Generalized Distributions Based on Alpha Power Transformation with Application to Cancer Data," Annals of Data Science, Springer, vol. 5(3), pages 421-436, September.
    • Handle: RePEc:spr:aodasc:v:5:y:2018:i:3:d:10.1007_s40745-018-0144-5
    DOI: 10.1007/s40745-018-0144-5
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    References listed on IDEAS

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    1. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    2. 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.
    3. Abbas Mahdavi & Debasis Kundu, 2017. "A new method for generating distributions with an application to exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6543-6557, July.
    4. Alzaatreh, Ayman & Famoye, Felix & Lee, Carl, 2014. "The gamma-normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 67-80.
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    Cited by:

    1. Hadeel S Klakattawi, 2022. "Survival analysis of cancer patients using a new extended Weibull distribution," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-20, February.

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