mvar2.1982Muirhead {SHT}

Two-sample Simultaneous Test of Mean and Variance by Muirhead Approximation (1982)

Description

Given two univariate samples x and y, it tests

H_0 : \mu_x = \mu_y, \sigma_x^2 = \sigma_y^2 \quad vs \quad H_1 : \textrm{ not } H_0

using Muirhead's approximation for small-sample problem.

Usage

mvar2.1982Muirhead(x, y)

Arguments

x

a length-n data vector.

y

a length-m data vector.

Value

a (list) object of S3 class htest containing:

statistic

a test statistic.

p.value

p-value under H_0.

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

References

Muirhead RJ (1982). Aspects of multivariate statistical theory, Wiley series in probability and mathematical statistics. Wiley, New York. ISBN 978-0-471-09442-5.

Examples

## CRAN-purpose small example
x = rnorm(10)
y = rnorm(10)
mvar2.1982Muirhead(x, y)

## Not run: 
## empirical Type 1 error 
niter   = 1000
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  x = rnorm(100)  # sample x from N(0,1)
  y = rnorm(100)  # sample y from N(0,1)
  
  counter[i] = ifelse(mvar2.1982Muirhead(x,y)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'mvar2.1982Muirhead'\n","*\n",
"* number of rejections   : ", sum(counter),"\n",
"* total number of trials : ", niter,"\n",
"* empirical Type 1 error : ",round(sum(counter/niter),5),"\n",sep=""))

## End(Not run)