SourceSet (version 0.1.1)

testMeanVariance: Test the equality of two normal distributions

Description

The function performs the test of equality of two multivariate normal distrbutions (class1 and class2).

Usage

testMeanVariance(S, S1, S2, n1, n2)

Arguments

S

estimated covariance matrix for pooled sample

S1

estimated covariance matrix in class 1

S2

estimated covariance matrix in class 2

n1

number of samples in class 1

n2

number of samples in class 2

Value

The function returns a list that contain the test statistic (stat) and the p-value test obtained of equality, using the asymptotic distribution (alpha).

Details

The criterion for testing the equality of two normal distributions is the following: $$\Lambda_c = n_1 * log( |S| / |S^1| ) + n_2 * log( |S| / |S^2| ) $$ The asymptotic null distribution of the criterion, when the maximum likelihood estimates of the covariance matrices are used, is Chi square with \( |\Gamma| * (|\Gamma|+3) / 2\) degrees of freedom, where G is the dimension of the underlying distributions.

See Also

parameters

Examples

# NOT RUN {
if(require(mvtnorm)){

  ## Generate two random samples of size 50 from two multivariate normal distributions
  # sample size
  n<-50
  # true parameters of class 1 and class 2
  param.class1<-simulation$condition1
  param.class2<-simulation$condition2$`5`$`2`
  # simulated dataset
  data.class1<-rmvnorm(n = n,mean =param.class1$mu ,sigma =param.class1$S)
  data.class2<-rmvnorm(n = n,mean =param.class2$mu ,sigma=param.class2$S)
  data<-rbind(data.class1,data.class2)
  classes<-c(rep(1,nrow(data.class1)),rep(2,nrow(data.class2)))

  s<-cov(data)
  s1<-cov(data.class1)
  s2<-cov(data.class2)
  testMeanVariance(S = s,S1 =s1, S2 = s2, n1 = n, n2 = n)

  ## equivalently...
  # estimated parameters: maximum likelihood estimate
  est.param<-parameters(data = data,classes =classes ,shrink = FALSE)
  testMeanVariance(est.param$S,est.param$S1,est.param$S2,est.param$n1,est.param$n2)
}
# }