kolmogorov.unif.test: Kolmogorov-Smirnov test for uniformity
Description
Performs Kolmogorov-Smirnov test for the hypothesis of uniformity, see Kolmogorov (1933).
Usage
kolmogorov.unif.test(x, nrepl=2000,k=0)
Arguments
x
a numeric vector of data values.
nrepl
the number of replications in Monte Carlo simulation.
k
variant the criterion.
Value
A list with class "htest" containing the following components:
statisticthe value of the Kolmogorov-Smirnov statistic.
p.valuethe p-value for the test.
methodthe character string "Kolmogorov-Smirnov test for uniformity".
data.namea character string giving the name(s) of the data.
Details
The Kolmogorov-Smirnov test for uniformity is based on the following statistics:
$$D^+ = max_i\left(x_i-\frac{i}{n+1}\right),\quad
D^- = max_i\left(\frac{i}{n+1}-x_i\right),\quad
D = max(D^+,D^-).$$
The p-value is computed by Monte Carlo simulation.
References
Kolmogorov A. (1933): Sulla determinazione empirica di una legge di distribuzione. --- G. Ist. Ital. Attuari, vol. 4, pp. 83--91.