Quantile

Usage

Quantile[list, q] gives the q quantile of list.
Quantile[list, {, , ... }] gives a list of quantiles , , ... .
Quantile[list, q, {{a, b}, {c, d}}] uses the quantile definition specified by parameters a, b, c, d.

Notes

Quantile[list, q] gives Sort[list, Less][[Ceiling[q Length[list]]]].
Quantile[{{, , ... }, {, , ... }, ... }, q] gives {Quantile[{, , ... }, q], Quantile[{, , ... }, 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 + d FractionalPart[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}}.
Quantile[list, q] always gives a result equal to an element of list.
• The same is true whenever .
• When , Quantile is piecewise linear as a function of .
Median[list] is equivalent to Quantile[list, 1/2, {{1/2, 0}, {0, 1}}].
• About ten different choices of parameters are in use in statistical work.
Quantile works with SparseArray objects.
• New in Version 5.

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