Quantile-based Chernoff distance for truncated random variables

Suchandan Kayal

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 20, 4938-4957

Abstract: Several probability distributions such as power-Pareto distribution (see Gilchrist 2000 and Hankin and Lee 2006), various forms of lambda distributions (see Ramberg and Schmeiser 1974 and Freimer et al. 1988), Govindarajulu distribution (see Nair, Sankaran, and Vineshkumar 2012), etc., do not have manageable distribution functions, though they have tractable quantile functions. Hence, analytical study of the properties of Chernoff distance of two random variables associated with these distributions via traditional distribution function-based tool becomes difficult. To make this simple, in this paper, we introduce quantile-based Chernoff distance for (left or right) truncated random variables and study its various properties. Some useful bounds as well as characterization results are obtained.

Date: 2018
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DOI: 10.1080/03610926.2017.1383426

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