John, > You can encapsulate mode, median and mean in a single formula. Suppose y is > a data vector and t is a scalar. The a value of t which minimizes > +/ (|y-t)^i [with special meaning for x^0: see below] is > - A mode of y if i=0. > -A median of y if i=1. > -The mean of y if i=2.
Neat! With a little calculus we can show that such a t satisfies ( (t>y) =&(+/@(#&(|y-t) ^ i-1:)) t<y ). So t is a "higher-order average" of sorts. This feels connected to distribution moments, but I don't immediately see the precise relationship. Thanks for sharing. > Here x^0 meas 1 if x=0 and 0 if x is nonzero. Hrm, I believe we want this the other way around. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
