A Generalization of the Quantile-Based Flattened Logistic Distribution

• Published in: Annals of data science Vol. 8; no. 3; pp. 603 - 627
• Main Authors: Chakrabarty, Tapan Kumar, Sharma, Dreamlee
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021; Springer Nature B.V
• Subjects: Artificial Intelligence; Business and Management; Data science; Economics; Finance; Goodness of fit; Insurance; Kurtosis; Management; Parameter estimation; PCB; Polychlorinated biphenyls; Quantiles; Random variables; Skewness; Statistics for Business; L-moment; Flattened generalized logistic distribution; order statistics; Asymptotic variance; Quantile function; Skewness-invariant kurtosis
• ISSN: 2198-5804; 2198-5812
• DOI: 10.1007/s40745-021-00322-3

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 r th 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.