G102 Kolmogorov Distribution

Function subprogram PROBKL calculates the Kolmogorov distribution function

$P(X)\; =\; -2\; \sum$_j=1^&inf; (-1)^jexp(-2j²X²)

for real arguments X.

Structure:

FUNCTION subprogram
User Entry Name: PROBKL

Usage:

In any arithmetic expression, PROBKL(X) has the value $P(X)$ ,

where PROBKL and X are of type REAL.

Method:

Direct evaluation or using functional relations.

Accuracy:

Approximately seven digits are correct. Results smaller than $10-40$ (corresponding to $X\; >\; 6.8116$ ) are set to zero. Note that the above formula has a statistical meaning only for "large" $N\; (>10)$ .

Notes:

1. For an experimental distribution with N events and a maximum deviation $\Delta N$ from a hypothetical distribution, $P(X)$ with $X=\; \Delta NN$ gives the confidence level for the null hypothesis.
2. To compare two experimental distributions with M and N events, respectively, one may use $X=M\; N/(M\; +\; N)\Delta N$ .

G103