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A Generalization of the Quantile-Based Flattened Logistic Distribution

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  • Tapan Kumar Chakrabarty

    (North Eastern Hill University)

  • Dreamlee Sharma

    (North Eastern Hill University
    Adamas University)

Abstract

In this paper, we propose a generalization of the quantile-based flattened logistic distribution Sharma and Chakrabarty (Commun Stat Theory Methods 48(14):3643–3662, 2019. https://doi.org/10.1080/03610926.2018.1481966 ). Having described the need for such a generalization from the data science perspective, several important properties of the distribution are derived here. We show that the rth order L-moment of the distribution can be written in a closed form expression. The L-skewness ratio and the L-kurtosis ratio of the distribution have been studied in detail. The distribution is shown to posses a skewness-invariant kurtosis measure based on quantiles and L-moments. The method of matching L-moments estimation has been used to estimate the parameters of the proposed model. The model has been applied to two real-life datasets and appropriate goodness-of-fit procedures have been used to test the validity of the model.

Suggested Citation

  • Tapan Kumar Chakrabarty & Dreamlee Sharma, 2021. "A Generalization of the Quantile-Based Flattened Logistic Distribution," Annals of Data Science, Springer, vol. 8(3), pages 603-627, September.
    • Handle: RePEc:spr:aodasc:v:8:y:2021:i:3:d:10.1007_s40745-021-00322-3
    DOI: 10.1007/s40745-021-00322-3
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    References listed on IDEAS

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    1. Bijamma Thomas & N.N. Midhu & P.G. Sankaran, 2015. "A software reliability model using mean residual quantile function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(7), pages 1442-1457, July.
    2. Balakrishnan, N. & So, H.Y., 2015. "A generalization of quantile-based skew logistic distribution of van Staden and King," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 44-51.
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    6. van Staden, Paul J. & King, Robert A.R., 2015. "The quantile-based skew logistic distribution," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 109-116.
    7. N.N. Midhu & P.G. Sankaran & N. Unnikrishnan Nair, 2014. "A Class of Distributions with Linear Hazard Quantile Function," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(17), pages 3674-3689, September.
    8. El-Sayed A. El-Sherpieny & Mamhoud M. Elsehetry, 2019. "Type II Kumaraswamy Half Logistic Family of Distributions with Applications to Exponential Model," Annals of Data Science, Springer, vol. 6(1), pages 1-20, March.
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