Quantile
Quantile[list,q]
gives the q quantile of list.
Quantile[list,{q1,q2,…}]
gives a list of quantiles q1, q2, ….
Quantile[list,q,{{a,b},{c,d}}]
uses the quantile definition specified by parameters a, b, c, d.
Quantile[dist,q]
gives a quantile of the distribution dist.
Details


- Quantile is also known as value at risk (VaR) or fractile.
- Quantile[list,q] gives Sort[list,Less][[Max[Ceiling[qLength[list]],1]]].
- Quantile[{{x1,y1,…},{x2,y2,…},…},q] gives {Quantile[{x1,x2,…},q],Quantile[{y1,y2,…},q]}.
- For a list of length n, Quantile[list,q,{{a,b},{c,d}}] depends on x=a+(n+b)q. If x is an integer, the result is s[[x]], where s=Sort[list,Less]. Otherwise, the result is s[[Floor[x]]]+(s[[Ceiling[x]]]-s[[Floor[x]]])(c+dFractionalPart[x]), with the indices taken to be 1 or n if they are out of range.
- The default choice of parameters is {{0,0},{1,0}}.
- Common choices of parameters include:
-
{{0, 0}, {1, 0}} inverse empirical CDF (default) {{0, 0}, {0, 1}} linear interpolation (California method) {{1/2, 0}, {0, 0}} element numbered closest to qn {{1/2, 0}, {0, 1}} linear interpolation (hydrologist method) {{0, 1}, {0, 1}} mean‐based estimate (Weibull method) {{1, -1}, {0, 1}} mode‐based estimate {{1/3, 1/3}, {0, 1}} median‐based estimate {{3/8, 1/4}, {0, 1}} normal distribution estimate - Quantile[list,q] always gives a result equal to an element of list.
- The same is true whenever d is 0.
- When d is 1, Quantile is piecewise linear as a function of q.
- Median[list] is equivalent to Quantile[list,1/2,{{1/2,0},{0,1}}].
- About 10 different choices of parameters are in use in statistical work.
- Quantile works with SparseArray objects.
- Quantile[dist,q] is equivalent to InverseCDF[dist,q].
Examples
open allclose allBasic Examples (6)
Scope (24)
Applications (7)
Properties & Relations (9)
Possible Issues (2)
Neat Examples (1)
See Also
Median Quartiles Ordering Variance MedianDeviation InterquartileRange Sort ListInterpolation Nearest InverseCDF InverseSurvivalFunction OrderDistribution
Tutorials
Related Guides
Related Links
Introduced in 2003
(5.0)
| Updated in 2007 (6.0)