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A Generalization of the Quantile-Based Flattened Logistic Distribution

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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.

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Acknowledgements

The second author acknowledges the Department of Science and Technology (DST), Government of India for her financial support through DST-INSPIRE fellowship with award no. IF130343. The authors also thank the anonymous reviewers for their valuable comments and suggestions which provided a great improvement to the manuscript.

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  1. Dreamlee Sharma

    Present address: Department of Mathematics, Adamas University, Kolkata, India

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  1. Department of Statistics, North Eastern Hill University, Meghalaya, India

    Tapan Kumar Chakrabarty & Dreamlee Sharma

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  1. Tapan Kumar Chakrabarty
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  2. Dreamlee Sharma
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Both the authors contributed equally.

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Correspondence to Dreamlee Sharma.

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Chakrabarty, T.K., Sharma, D. A Generalization of the Quantile-Based Flattened Logistic Distribution. Ann. Data. Sci. 8, 603–627 (2021). https://doi.org/10.1007/s40745-021-00322-3

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  • DOI: https://doi.org/10.1007/s40745-021-00322-3

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