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RankedMin

RankedMin
gives the n^(th) smallest element in list.
  • RankedMin yields a definite result if all its arguments are real numbers.
The second smallest of three numbers:
The second smallest of three numbers:
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Click for copyable input
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RankedMin works with approximate numeric quantities:
And exact numeric quantities:
Basic symbolic simplification is done automatically:
Expand into a Piecewise function:
Integrate expressions involving RankedMin:
Solve equations and inequalities:
Plot the bivariate RankedMin functions:
Plot the contours of bivariate and trivariate RankedMin functions:
RankedMin 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:
RankedMin is equivalent to Min:
RankedMin is equivalent to Max:
RankedMin is equivalent to RankedMax:
RankedMin is equivalent to Quantile:
RankedMin is equivalent to Sort[{x1, ..., xn}]k:
The equivalent Piecewise function has disjoint piecewise case domains:
Algebraically prove the piecewise case domains are disjoint:
Visually show it:
Algebraically prove the piecewise case domains are pairwise disjoint:
Visually show it:
Two-dimensional sublevel sets:
Three-dimensional sublevel sets:
New in 8