g01ey returns the upper tail probability associated with the one sample Kolmogorov–Smirnov distribution.


public static double g01ey(
	int n,
	double d,
	out int ifail
Visual Basic
Public Shared Function g01ey ( _
	n As Integer, _
	d As Double, _
	<OutAttribute> ByRef ifail As Integer _
) As Double
Visual C++
static double g01ey(
	int n, 
	double d, 
	[OutAttribute] int% ifail
static member g01ey : 
        n : int * 
        d : float * 
        ifail : int byref -> float 


Type: System..::..Int32
On entry: n, the number of observations in the sample.
Constraint: n1.
Type: System..::..Double
On entry: contains the test statistic, Dn+ or Dn-.
Constraint: 0.0d1.0.
Type: System..::..Int32%
On exit: ifail=0 unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Return Value

g01ey returns the upper tail probability associated with the one sample Kolmogorov–Smirnov distribution.


Let Snx be the sample cumulative distribution function and F0x the hypothesised theoretical distribution function.
g01ey returns the upper tail probability, p, associated with the one-sided Kolmogorov–Smirnov test statistic Dn+ or Dn-, where these one-sided statistics are defined as follows;
If n100 an exact method is used; for the details see Conover (1980). Otherwise a large sample approximation derived by Smirnov is used; see Feller (1948)Kendall and Stuart (1973) or Smirnov (1948).


Conover W J (1980) Practical Nonparametric Statistics Wiley
Feller W (1948) On the Kolmogorov–Smirnov limit theorems for empirical distributions Ann. Math. Statist. 19 179–181
Kendall M G and Stuart A (1973) The Advanced Theory of Statistics (Volume 2) (3rd Edition) Griffin
Siegel S (1956) Non-parametric Statistics for the Behavioral Sciences McGraw–Hill
Smirnov N (1948) Table for estimating the goodness of fit of empirical distributions Ann. Math. Statist. 19 279–281

Error Indicators and Warnings

Errors or warnings detected by the method:
On entry,n<1.
On entry,d<0.0,
An error occured, see message report.


The large sample distribution used as an approximation to the exact distribution should have a relative error of less than 2.5% for most cases.

Parallelism and Performance


Further Comments

The upper tail probability for the two-sided statistic, Dn=maxDn+,Dn-, can be approximated by twice the probability returned via g01ey, that is 2p. (Note that if the probability from g01ey is greater than 0.5 then the two-sided probability should be truncated to 1.0). This approximation to the tail probability for Dn is good for small probabilities, (e.g., p0.10) but becomes very poor for larger probabilities.
The time taken by the method increases with n, until n>100. At this point the approximation is used and the time decreases significantly. The time then increases again modestly with n.


The following example reads in 10 different sample sizes and values for the test statistic Dn. The upper tail probability is computed and printed for each case.

Example program (C#): g01eye.cs

Example program data: g01eye.d

Example program results: g01eye.r

See Also