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MathGroup Archive 2000

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Exact Kolmogorov Test Distribution; Computing Times

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21630] Exact Kolmogorov Test Distribution; Computing Times
  • From: "Hermann Meier" <hmeier at webshuttle.ch>
  • Date: Tue, 18 Jan 2000 02:35:16 -0500 (EST)
  • Organization: EUnet AG, Switzerland. A KPNQwest Company.
  • Sender: owner-wri-mathgroup at wolfram.com

The following program computes the exact distribution of the one-sample
Kolmogorov test stastistic (two-sided; see Birnbaum, Journal of the American
Statistical Association, Vol. 47, 1952, p. 425-441):

R[0, 0][y_] = 1;
R[j_, 0][y_] /; j != 0 = 0;
R[j_, k_][y_] /; Abs[j] >= y = 0;
R[j_, k_][y_] /; Abs[j] <= y - 1 := R[j, k][y] =
    Exp[-1]*Sum[R[j + 1 - i, k - 1][y]/i!, {i, 0, 2*y - 1}];

cdfkolmog[n_,y_] := n!*Exp[n]*R[0, n][y]/n^n


Computing times (2x450 MHZ Pentium, 256 MB, Windows NT 4 SP 6):

N[cdfkolmog[50, 15]]//Timing
{8.235 Second, 0.9998264674}

(To compute all R's from scratch, I use Clear[R] and evaluate the first
program lines once more):
N[cdfkolmog[100,15]]//Timing
{26.172 Second, 0.9801607579}

Is there a possibility to speed up this programm (retaining infinite
precision) ? I would appreciate any suggestion.

With kind regards
Hermann Meier

























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