A general approximation to quantiles

Chang Yu and Daniel Zelterman

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 19, 9834-9841

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.

Date: 2017
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DOI: 10.1080/03610926.2016.1222433

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