RankedMin
RankedMin[list,n]
gives the n smallest element in list.
RankedMin[list,-n]
gives the n largest element in list.
Details

- RankedMin yields a definite result if all its arguments are real numbers.
- RankedMin[{x1,…,xm},n] is often indicated using
or
.
- RankedMin[{x1,…,xm},1] is equivalent to Min[{x1,…,xm}].
- RankedMin[{x1,…,xm},-1] is equivalent to Max[{x1,…,xm}].
- RankedMin[{x1,…,xm},m] is equivalent to Max[{x1,…,xm}].
- RankedMin[{x1,…,xm},n] is equivalent to Quantile[{x1,…,xm},n/m].
Examples
open allclose allBasic Examples (3)
Scope (17)
Numerical Evaluation (4)
Specific Values (4)
Visualization (3)
Function Properties (3)
Applications (7)
Plot the bivariate RankedMin functions:
Plot the contours of bivariate and trivariate RankedMin functions:
RankedMin[{y1,…,yn,x},k] as a function of x:
Compute the expectation of the second smallest (median) variable:
Alternatively, use OrderDistribution:
Compute the probability of the second smallest variable being less than 1:
Show that OrderDistribution is a special case of TransformedDistribution:
Properties & Relations (6)
RankedMin[{x1,…,xn},1] is equivalent to Min[x1,…,xn]: »
RankedMin[{x1,…,xn},n] is equivalent to Max[x1,…,xn]: »
RankedMin[{x1,…,xn},k] is equivalent to RankedMax[{x1,…,xn},n-k+1]:
RankedMin[{x1,…,xn},m] is equivalent to Quantile[{x1,…,xn},m/n]: »
RankedMin[{x1,…,xn},k] is equivalent to Sort[{x1,…,xn}]〚k〛:
The equivalent Piecewise function has disjoint piecewise case domains:
Algebraically prove the piecewise case domains are disjoint:
Algebraically prove the piecewise case domains are pairwise disjoint:
Text
Wolfram Research (2010), RankedMin, Wolfram Language function, https://reference.wolfram.com/language/ref/RankedMin.html (updated 2017).
BibTeX
BibLaTeX
CMS
Wolfram Language. 2010. "RankedMin." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/RankedMin.html.
APA
Wolfram Language. (2010). RankedMin. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RankedMin.html