# simplex.uniform: Probability Simplex : Tests of Uniformity In SHT: Statistical Hypothesis Testing Toolbox

 simplex.uniform R Documentation

## 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 Δ_{p-1} =\lbrace z \in \mathbb{R}^p~|~z_j > 0, ∑_{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 LRTlikelihood-ratio test with the Dirichlet distribution. LRTsymlikelihood-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")



SHT documentation built on Nov. 3, 2022, 9:06 a.m.