Re: KS Analysis In Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg49290] Re: [mg49286] KS Analysis In Mathematica
• From: "Christos Argyropoulos MD" <chrisarg at medscape.com>
• Date: Mon, 12 Jul 2004 02:11:31 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi,
Try the following url
http://www.verbeia.com/mathematica/mathecon/othercode.html
if you are after for a "Normality" test and other goodies.
Alternatively try the following Mathematica Code:
-------------------------------------------------------------
Needs["Statistics`DescriptiveStatistics`"];
Needs["Statistics`DataManipulation`"];
Needs["Statistics`ContinuousDistributions`"];
Needs["Statistics`DescriptiveStatistics`"];
Needs["Statistics`ConfidenceIntervals`"];
Needs["Statistics`MultiDescriptiveStatistics`"];
Q[s_] := Module[{r}, Sum[(r - s)^r*(x^r)/r!, {r, 0, Floor[s]}]]
F[s_, m_] := Normal[Series[Simplify[(Q[s]^2)/Q[2*s]], {x, 0, m}]]
Kolmogorov[d_, m_] := Min[N[Abs[Coefficient[F[m*d, m], x, m]*m!/
(m^m)]], 1]
Lillefors[y_List] := Module[{stand, quant,
kolm}, stand = Standardize[y]; quant = Transpose[QuantileForm
[stand]];
kolm = N[Max[Abs[quant[[1]] -
Map[CDF[NormalDistribution[0, 1], #] &, quant[[2]]]]]]]
-------------------------------------------------------------
Kolmogorov[d,m] gives the Probability of the Kolmogorov Smirnov Test
when the test statistic value is d and the sample tested is of size m.
If you want to test whether a list of observations has come from a
Normal Distribution with unknow mean and variance, use the function
Lillefors[obs] which calculates the P-value based on the Lillefors
modification of the KS statistic.
Cheers
Christos Argyropoulos

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