Bonjour Leo,
The distance in question is between Fn and F. Those are respectively the
"empirical" cumulative distribution and the model's or theoretical
cumulative distribution.
Fn is defined as follows: Fn(x) = (1/n)*(#Xi's that are less than or equal
to x)
So if your sample is 5, 2, 9, 12, 2
then Fn(x) = 0 if x < 2
= 0.4 if 2 <= x < 5
= 0.6 if 5 <= x < 9
= 0.8 if 9 <= x < 12
= 1.0 if 12 <= x
For an example of calculation of F, I'll take an Exponential with mean 1
So the density is f(x) = exp(-x) for x>0
and the CDF is F(x) = 1-exp(-x) for x>0
So to calculate the KS stat, you need to evaluate F at the points from the
sample (2, 5, 9 and 12)
and compare with the values of Fn at the corresponding points and the values
of Fn just before the corresponding point.
i.e. in this example, you would take the maximum of all the following:
|1-exp(-2) - 0.0|
|1-exp(-2) - 0.4|
|1-exp(-5) - 0.4|
|1-exp(-5) - 0.6|
|1-exp(-9) - 0.6|
|1-exp(-9) - 0.8|
|1-exp(-12) - 0.8|
|1-exp(-12) - 1.0|
--
------------------------------------------------------------------
Jacques Rioux Ph. D. ASA
Associate Professor of Actuarial Science
College of Business and Public Administration
Drake University
2507 University Ave
Des Moines, IA, 50311
Tel: 515-271-1894
Fax: 515-271-4518
"Leo, Durancel" <[EMAIL PROTECTED]> wrote in message
a98kfj$9uv$[EMAIL PROTECTED]">news:a98kfj$9uv$[EMAIL PROTECTED]...
> Hello,
>
> In th K-S we have to take distance between points of two curves.
> I would known how we take this points. Do i exactly understand that is
> values of cumulatives functions for the experimental sample and for the
> distribution. That is alright ?
> In this case can anyone give a example for cumulative values for few
points
> of an experimental sample and for theoritical values of a distribution
> (Normal for example) ?
>
> Thank you
>
> Leo
> --
>
>
.
.
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