mvar1.1998AS {SHT}

One-sample Simultaneous Test of Mean and Variance by Arnold and Shavelle (1998)

Description

Given two univariate samples x and y, it tests

H_0 : \mu_x = \mu_0, \sigma_x^2 = \sigma_0^2 \quad vs \quad H_1 : \textrm{ not } H_0

using asymptotic likelihood ratio test.

Usage

mvar1.1998AS(x, mu0 = 0, var0 = 1)

Arguments

x

a length-n data vector.

mu0

hypothesized mean \mu_0.

var0

hypothesized variance \sigma_0^2.

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

Arnold BC, Shavelle RM (1998). “Joint Confidence Sets for the Mean and Variance of a Normal Distribution.” The American Statistician, 52(2), 133–140.

Examples

## CRAN-purpose small example
mvar1.1998AS(rnorm(10))

## 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)
  
  counter[i] = ifelse(mvar1.1998AS(x)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'mvar1.1998AS'\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)