R: Quantile of some uniformity tests

unif.test.quantile {DiceDesign} | R Documentation

## Quantile of some uniformity tests

### Description

Computes the quantile of a uniformity test at a given significance level (see available tests and levels below).

### Usage

    unif.test.quantile(type, n, alpha)

### Arguments

`type` | a character indicating which test is used. The choices are the following: "greenwood", "qm" (for Quesenberry-Miller), "ks" (Kolmogorov-Smirnov), "cvm" (Cramer-Von Mises) and "V" (D+ + D- from Kolmogorov-Smirnov).
`n` | an integer equal to the sample size.
`alpha` | a real number equal to significance level. At present stage, only four values are available: 0.1, 0.05, 0.025 and 0.01.

### Details

Modified statistics are used. For `alpha = 0.05`, the quantile is (see D Agostino and Stephens, 1986, section 4.4.): `1.358/(sqrt(n) + 0.12 + 0.11/sqrt(n))` for Kolmogorov-Smirnov and `0.461/(1+1/n) + 0.4/n - 0.6/n^2` for Cramer-von Mises. When the design size is `< 20`, the corrected value seems to be a good approximation, but the non asymptotical value should be preferred.

### Value

A real number equal to the quantile of the specified test at significance level `alpha` for `n` observations.

### Author(s)

O. Roustant

### References

D Agostino R.B., Stephens M.A. (1986), Goodness-of-fit techniques, CRC Press, New York.

### See Also

`unif.test.statistic`, `rss2d`, `rss3d`

[Package DiceDesign version 1.9 Index]