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. • New in Version 5.
|
