# pkolm: Kolmogorov Dn Distribution In kolmim: An Improved Evaluation of Kolmogorov's Distribution

## Description

Cumulative distribution function for Kolmogorov's goodness-of-fit measure.

## Usage

 `1` ```pkolm(d, n) ```

## Arguments

 `d` the argument for the cumulative distribution function of Dn. `n` the number of variates.

## Details

Given an ordered set of `n` standard uniform variates, x_1 < … < x_n, Kolmogorov suggested D_n = \max[D_n^-, D_n^+] as a goodness-of-fit measure, where: D_n^- = \max_{i=1, … n} [x_i - (i - 1) / n] and D_n^+ = \max_{i=1, … n} [i / n - x_i].

`pkolm` provides the original algorithm proposed by Wang, Tsang, and Marsaglia (2003) to compute the cumulative distribution function K(n, d) = P(D_n < d). This routine is used by `ks.test` (package `stats`) for one-sample two-sided exact tests, and it is implemented in the C routine `pkolmogorov2x`. `pkolm` is a simple wrap around `pkolmogorov2x`.

## Value

Returns K(n, d) = P(D_n < d).

## Source

The two-sided one-sample distribution comes via Wang, Tsang, and Marsaglia (2003).

## References

George Marsaglia, Wai Wan Tsang and Jingbo Wang (2003), Evaluating Kolmogorov's distribution. Journal of Statistical Software, 8/18. http://www.jstatsoft.org/v08/i18/.

`pkolmim` for an improved routine to compute K(n, d), and `ks.test` for the Kolmogorov-Smirnov test.

## Examples

 ```1 2 3 4 5 6 7 8``` ```n <- 100 x <- 1:100 / 500 plot(x, sapply(x, function (x) pkolm(x, n)), type='l') # Wang et al. approximation s <- x ^ 2 * n ps <- pmax(0, 1 - 2 * exp(-(2.000071 + .331 / sqrt(n) + 1.409 / n) * s)) lines(x, ps, lty=2) ```

### Example output ```
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kolmim documentation built on May 2, 2019, 2:26 p.m.