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.

O. Roustant

### References

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

unif.test.statistic, rss2d, rss3d