Re: Mann-Kendall test statistic
From: Dr. Knud Werner (kwe_at_probits.de)
Date: 09/29/04
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Date: Wed, 29 Sep 2004 08:31:31 +0100
Glen wrote:
>
> "Dr. Knud Werner" <kwe@probits.de> wrote in message news:<4159DC8C.2FDB1677@probits.de>...
> > Hello,
> >
> > I'm interested in calculating the Mann-Kendall test statistics
> > for a real sequence and would like to know whether someone knows
> > about pointers to methods of calculating it in O(n log(n)) instead
> > of O(n^2).
>
> Google seems to turn up several things called "Mann-Kendall" that
> don't all look to be quite the same thing. Can you be more specific,
> perhaps giving a description of the statistic you're interested in?
>
> Glen
AFAIK the ordinary Mann-Kendall test statistics for a real sequence
y = (y_1,\ldots,y_n) is calculated as
S = \Sum_{i=1}^{n-1} \Sum_{j=i+1}^n sgn(y_j - y_i)
ie. it is the sum of the signs of all pairwise differences. If eg.
you have the sequence (1,2,3,4,5,6,7,8,9,10) there are 45 pairs,
each contributing a +1, giving the test statistics of +45.
Best regards
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