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Quantile Function

A quantile function of a random variable X is a generalized inverse of its distribution function F_X. A standard convention defines

Q(p)=inf{x in R:F_X(x)>=p},

for 0<p<1. If F_X is continuous and strictly increasing, then Q(p) is the unique value x satisfying F_X(x)=p. The generalized-inverse definition remains valid for discrete distributions and other cases in which F_X has jumps or constant intervals.

See also

Continuous Distribution, Discrete Distribution, Distribution Function, Probability, Quantile, Strictly Increasing Function, Random Variable

Portions of this entry contributed by Christopher Stover

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References

Hyndman, R. J. and Fan, Y. "Sample Quantiles in Statistical Packages." Amer. Stat. 50, 361-365, 1996.Shaw, W. "Refinement of the Normal Quantile: A Benchmark Normal Quantile Based on Recursion, and an Appraisal of the Beasley-Springer-Moro, Acklam, and Wichura (AS241) Methods." 2007. http://www.mth.kcl.ac.uk/~shaww/web_page/papers/NormalQuantile1.pdf.

Referenced on Wolfram|Alpha

Quantile Function

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Quantile Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/QuantileFunction.html

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