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

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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.

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Acknowledgements

The authors are grateful for the comments and suggestions by the referees and the Associate Editor. Their comments and suggestions have greatly improved the paper.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, Egypt

    M. Nassar, O. Abo-Kasem & M. Mead

  2. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE

    A. Alzaatreh

  3. Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

    M. Mansoor

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  1. M. Nassar
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  2. A. Alzaatreh
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  3. O. Abo-Kasem
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  4. M. Mead
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  5. M. Mansoor
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Correspondence to A. Alzaatreh.

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Nassar, M., Alzaatreh, A., Abo-Kasem, O. et al. A New Family of Generalized Distributions Based on Alpha Power Transformation with Application to Cancer Data. Ann. Data. Sci. 5, 421–436 (2018). https://doi.org/10.1007/s40745-018-0144-5

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  • DOI: https://doi.org/10.1007/s40745-018-0144-5

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