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A general approximation to quantiles

Author

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  • Chang Yu
  • Daniel Zelterman

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.

Suggested Citation

  • Chang Yu & Daniel Zelterman, 2017. "A general approximation to quantiles," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(19), pages 9834-9841, October.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:19:p:9834-9841
    DOI: 10.1080/03610926.2016.1222433
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