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% Kuiper Tests
%
% This is asymptotically correct
private define kuiper_test_prob (n, d)
{
variable sn = sqrt(n);
variable factor = sn + 0.155 + 0.24/sn;
d = factor * d;
if (d < 0.4)
return 1.0;
if (d > 20.0)
return 0.0;
variable x = ([1:100]*d)^2;
variable p = 2.0*sum ((4.0*x - 1.0) * exp (-2.0*x));
if (p < 0.0)
p = 0.0;
if (p > 1.0)
p = 1.0;
return p;
}
define kuiper_test ()
{
variable d_ref = NULL;
if (_NARGS == 2)
d_ref = ();
else if (_NARGS != 1)
usage ("p = kuiper_test (CDF [,&D]); %% 1-sample Kuiper test\n",
+ " Here CDF are the expected CDFs at the corresponding random points.");
variable cdf = ();
cdf = __tmp(cdf)[array_sort(cdf)];
variable n = length (cdf);
variable nn = 1.0*n;
variable dplus = max ([1:n]/nn - cdf);
variable dminus = max (cdf-[0:n-1]/nn);
variable d = dplus + dminus;
if (d_ref != NULL)
@d_ref = d;
return kuiper_test_prob (n, d);
}
define kuiper_test2 ()
{
variable d_ref = NULL;
if (_NARGS == 3)
d_ref = ();
else if (_NARGS != 2)
usage ("p = %s(X1, X2 [,&D]); %% Two-sample Kuiper test", _function_name ());
variable xm, xn; (xm, xn) = ();
variable x = [xn, xm];
variable n = length (xn);
variable m = length (xm);
variable mn = m + n;
variable c = Int_Type[mn];
c[[0:n-1]] = 1;
variable i = array_sort (x);
x = x[i];
c = c[i]; c = cumsum (__tmp(c));
variable dmn = (c/n - [1:mn]/(mn*1.0));
variable factor = mn/(m*1.0);
variable dplus = factor * max(dmn);
variable dminus = factor * min(dmn);
variable d = dplus - dminus;
if (d_ref != NULL)
@d_ref = d;
return kuiper_test_prob (double(m)*double(n)/double(mn), d);
}
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