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An Extension of J-Shaped Distribution with Application to Tissue Damage Proportions in Blood

Author

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  • Komal Shekhawat

    (Institute of Infrastructure, Technology Research and Management (IITRAM))

  • Vikas Kumar Sharma

    (Institute of Infrastructure, Technology Research and Management (IITRAM)
    Institute of Science, Banaras Hindu University (BHU))

Abstract

In this paper, we introduce a two parameter extension of J-shaped distribution investigated by Topp and Leone (J. Am. Stat. Assoc. 50, 209–219, 1995) which is defined on the unit interval. We explicitly derive the closed-form expressions of the moments, mode and quantiles of the proposed distribution. L-moments and coefficients of skewness and kurtosis are obtained using the quantile function. Other important properties including identifiability, entropy, stochastic orderings, stress-strength reliability and differential equations associated with the distribution are also discussed. We construct maximum likelihood estimators to estimate the distribution parameters that are unknown for a given set of practical data. An extensive simulation study is carried out to study the behaviors of mean squared error, bias and absolute bias of the maximum likelihood estimators. An application of modeling tissue damage proportions in blood at various concentration levels of a drug is presented to show the adequacy of the proposed distribution over the unit range distributions existing in the literature. A parametric regression model based on the proposed distribution is introduced and the goodness-of-fit results are compared with that of Beta regression model.

Suggested Citation

  • Komal Shekhawat & Vikas Kumar Sharma, 2021. "An Extension of J-Shaped Distribution with Application to Tissue Damage Proportions in Blood," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 548-574, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-019-00218-6
    DOI: 10.1007/s13571-019-00218-6
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    References listed on IDEAS

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    1. M. E. Ghitany & S. Kotz & M. Xie, 2005. "On some reliability measures and their stochastic orderings for the Topp-Leone distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 715-722.
    2. Vikas Kumar Sharma & Sanjay Kumar Singh & Umesh Singh & Faton Merovci, 2016. "The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5709-5729, October.
    3. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    4. 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.
    5. Morad Alizadeh & Fazlollah Lak & Mahdi Rasekhi & Thiago G. Ramires & Haitham M. Yousof & Emrah Altun, 2018. "The odd log-logistic Topp–Leone G family of distributions: heteroscedastic regression models and applications," Computational Statistics, Springer, vol. 33(3), pages 1217-1244, September.
    6. Saralees Nadarajah & Samuel Kotz, 2003. "Moments of some J-shaped distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 311-317.
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