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A goodness-of-fit test for any statistical distribution. The test relies on the fact that the value of the sample cumulative
density function is asymptotically normally distributed.
To apply the Kolmogorov-Smirnov test, calculate the cumulative frequency (normalized by the sample size) of the observations as a function of class. Then calculate the
cumulative frequency for a true distribution (most commonly, the normal distribution). Find the greatest discrepancy between
the observed and expected cumulative frequencies, which is called the "D-statistic." Compare this against the critical D-statistic for that sample size. If the calculated D-statistic is greater than the critical one, then reject the
null hypothesis that the distribution
is of the expected form. The test is an R-estimate.
Boes, D. C.; Graybill, F. A.; and Mood, A. M. Introduction to the Theory of Statistics, 3rd ed. New York:
McGraw-Hill, 1974.
DeGroot, M. H. Ch. 9 in Probability and Statistics, 3rd ed. Reading, MA: Addison-Wesley,
1991.
Knuth, D. E. §3.3.1B in The Art of Computer Programming, Vol. 2: Seminumerical Algorithms,
3rd ed. Reading, MA: Addison-Wesley, pp. 45-52, 1998.
 Neal, D. K. "Goodness of Fit Tests for Normality."
Mathematica Educ. Res. 5, 23-30, 1996. http://library.wolfram.com/infocenter/Articles/1379/.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Kolmogorov-Smirnov Test." In Numerical Recipes in FORTRAN: The Art of Scientific Computing,
2nd ed. Cambridge, England: Cambridge University Press, pp. 617-620,
1992.
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