See also
Continuous Distribution,
Discrete Distribution,
Distribution
Function,
Probability,
Quantile,
Random Variable,
Strictly
Increasing Function
Portions of this entry contributed by Christopher
Stover
Explore with Wolfram|Alpha
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. https://web.archive.org/web/20070609171237if_/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
Subject classifications
is a generalized inverse of its distribution
function 
.
A standard convention defines
.
If 
is continuous and strictly
increasing, then 
is the unique value 
satisfying 
. The generalized-inverse definition remains valid for
discrete distributions and other cases in
which 
has jumps or constant intervals.
