R: Murakami test statistic distribution.

murakami_cdf {BWStest} | R Documentation

## Murakami test statistic distribution.

### Description

Estimates the CDF of the Murakami test statistics via permutations.

### Usage

    murakami_cdf(B, n1, n2, flavor = 0L, lower_tail = TRUE)

### Arguments

`B` | the Murakami test statistic or a vector of the same.
`n1` | number of elements in the first sample.
`n2` | number of elements in the second sample.
`flavor` | the 'flavor' of the test statistic. See `murakami_stat`.
`lower_tail` | boolean, when `TRUE` returns the CDF, Psi, otherwise compute the upper tail, 1 - Psi, which is potentially more useful for hypothesis tests.

### Details

Given the Murakami test statistic B_j for 0 <= j <= 5, computes the CDF under the null that the two samples come from the same distribution. The CDF is computed by permutation test and memoization.

### Value

a vector of the same size as `B` of the CDF under the null.

### Note

the CDF is approximately computed by evaluating the permutations up to some reasonably small sample size (currently the cutoff is 9). When larger sample sizes are used, the distribution of the test statistic may not converge. This is apparently seen in flavors 3 through 5.

### Author(s)

Steven E. Pav shabbychef@gmail.com

### References

W. Baumgartner, P. Weiss, H. Schindler, 'A nonparametric test for the general two-sample problem', Biometrics 54, no. 3 (Sep., 1998): pp. 1129-1135. http://doai.io/10.2307/2533862

M. Neuhauser, 'Exact tests based on the Baumgartner-Weiss-Schindler Statistic–a survey', Statistical Papers 46, no. 1 (2005): pp. 1-30. http://doai.io/10.1007/BF02762032

M. Neuhauser, 'One-sided two-sample and trend tests based on a modified Baumgartner-Weiss-Schindler statistic', J. Nonparametric Statistics 13, no. 5 (2001): pp 729-739. http://doai.io/10.1080/10485250108832874

H. Murakami, 'K-sample rank test based on modified Baumgartner statistic and its power comparison', J. Jpn. Comp. Statist. 19, no. 1 (2006): pp. 1-13. http://doai.io/10.5183/jjscs1988.19.1

H. Murakami, 'Modified Baumgartner Statistics for the two-sample and multisample problems: a numerical comparison', J. Stat. Comp. and Sim. 82, no. 5 (2012): pp. 711-728. http://doai.io/10.1080/00949655.2010.551516

H. Murakami, 'Lepage type statistic based on the modified Baumgartner statistic', Comp. Stat. & Data Analysis 51 (2007): pp 5061-5067. http://doai.io/10.1016/j.csda.2006.04.026

### See Also

`murakami_stat`.

### Examples

    # basic usage:
    xv <- seq(0,4,length.out=101)
    yv <- murakami_cdf(xv, n1=8, n2=6, flavor=1L)
    plot(xv,yv)
    zv <- bws_cdf(xv)
    lines(xv,zv,col='red')

    # check under the null:
    ## Not run:
    flavor <- 1L
    n1 <- 8
    n2 <- 8
    set.seed(1234)
    Bvals <- replicate(2000,murakami_stat(rnorm(n1),rnorm(n2),flavor))
    # should be uniform:
    plot(ecdf(murakami_cdf(Bvals,n1,n2,flavor)))

    ## End(Not run)

[Package BWStest version 0.2.2 Index]