simplex.uniform {SHT}

Probability Simplex : Tests of Uniformity

Description

Given a data $X \in \mathbb{R}{n\times p}$ such that its rows are vectors in a probability simplex, i.e., $x \in \Delta_{p-1} =\lbrace z \in \mathbb{R}^p~|~z_j > 0, \sum_{i=1}^p z_i = 1 \rbrace,$ test whether the data is uniformly distributed.

Usage

simplex.uniform(X, method)

Arguments

X

an $(n\times p)$ data matrix where each row is an observation.

method

(case-insensitive) name of the method to be used, including

LRT

likelihood-ratio test with the Dirichlet distribution.

LRTsym

likelihood-ratio test using the symmetric Dirichlet distribution (default).

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.

Examples

## pseudo-uniform data generation
N = 100
P = 4
X = matrix(stats::rnorm(N*P), ncol=P)
for (n in 1:N){
  x = X[n,]
  x = abs(x/sqrt(sum(x^2)))
  X[n,] = x^2
}

## run the tests
simplex.uniform(X, "LRT")
simplex.uniform(X, "lrtsym")