A general approximation to quantiles. Issue 19 (2nd October 2017)

• Record Type: Journal Article
• Authors: Yu, Chang; Zelterman, Daniel
• Is Part Of: Communications in statistics. Volume 46:Issue 19(2017)
• Page Start: 9834
• Page End: 9841
• Publication Date: 2017-10-02
• Subjects: Inverse distribution function -- percentage points -- Taylor expansion; Primary: 62E17, 65D20 -- Secondary: 65D15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2016.1222433
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: For many continuous distributions, a closed-form expression for their quantiles does not exist. Numerical approximations for their quantiles are developed on a distribution-by-distribution basis. This work develops a general approximation for quantiles using the Taylor expansion. Our method only requires that the distribution has a continuous probability density function and its derivatives can be derived to a certain order (usually 3 or 4). We demonstrate our unified approach by approximating the quantiles of the normal, exponential, and chi-square distributions. The approximation works well for these distributions.