RE: st: ksmirnov

["Guessab Houda" <houda.guessab@gre.generali.com>]

Nick told me that it's not correct to use kormogolv smirnov to compare the shape of series with a student distribution, is there another numerical method (not graphical)to do that?

Thank you very much maarten for you help!

Houda GUESSAB

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten Buis
Sent: mardi 21 août 2012 12:27
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: ksmirnov

On Tue, Aug 21, 2012 at 11:40 AM, Guessab Houda wrote:
> I mean how can I say that the distribution is more or less similar to student with 8 degrees?

For that I typically like to add a portfolio of simulated variables
that were drawn from the distribution of interest. That way you can
get an informal idea of how much variation on can reasonably expect if
your model (a student t-distribution with 8 degrees of freedom) is
true.

*------------------ begin example -------------------
sysuse auto, clear
egen rank = rank(mpg), unique
su rank, meanonly
gen expected = -invttail(8, (rank - 0.5) / `r(max)')
su mpg
local mean = r(mean)
local sd = r(sd)

 mata
 void function dangerous_sort(string scalar var,
                              string scalar touse) {
	real matrix x
	st_view(x =., ., var, touse)
	x[.,.] = x[order(x,1)]
}
end
gen byte touse = 1

sort expected
forvalues i = 1/10 {
	gen sim`i' = rt(8)*`sd'/sqrt(4/3) + `mean'
	mata: dangerous_sort("sim`i'", "touse")
	local lpattern "`lpattern' solid"
	local lcolor "`lcolor' gs8"
}
local lpattern "lpattern(`lpattern')"
local lcolor "lcolor(`lcolor')"

twoway line sim* expected,                    ///
    `lcolor' `lpattern'                    || ///
scatter mpg expected, mstyle(p1)           || ///
function t_8 = `mean' + x * `sd' / sqrt(4/3), ///
    ra(expected) lstyle(refline)              ///
    legend(order(1  "simulation"              ///
                 11 "observed"                ///
                 12 "reference"))
*------------------- end example --------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
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