Piano wrote in news:[EMAIL PROTECTED]:
> Let F(x) be Gaussian cdf, and f(x) be the density.
>
> According to Abramowitz and Stegum p954, if x is observed with small
> error,
> Delta F(x)=f(x) Delta x
> where Delta x is the difference operator.
>
> Let x be a vector of N(0,1) variables sorted from smallest to largest.
> I am interested in the difference between the CDF of two consecutive
> (normal) variables in the ordered sequence. say, j and j-1. The A-S
> result suggests F(j)-F(j-1)= f(j) [x(j)-x(j-1)]
>
> But this seems to suggest F(x) for the ordered series is a random
> walk. Is this a correct use of A-S, and is this a known result?
>
Looks like a version of the Fundamental Theorem of Calculus to me.
Nothing to do with random walks per se. The probability density, f(x), is
the first derivative of the cumulative distribution. But in the case of a
generalization to discrete distributions that you propose, the
singularities may cause difficulties. f(x) might not be well defined for
discrete distributions.
That page of A-S (1964) deals with table interpolation. Perhaps you are
using a different edition.
--
David Winsemius
If the statistics are boring, then you've got the wrong numbers.
-Edward Tufte
.
.
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