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Commun Stat Theory Methods. 2017;46(19):9834-9841. doi: 10.1080/03610926.2016.1222433. Epub 2017 Jul 10.

A general approximation to quantiles.

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Department of Biostatistics, Vanderbilt University School of Medicine, Nashville, TN 37232, U.S.A.
Department of Biostatistics, Yale University School of Public Health New Haven, CT 06520, U.S.A.


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.


Inverse distribution function; Percentage points; Taylor expansion

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