Comparison of different concentration parameters based on probability mass function.

This function provides a graphical display to compare different concentration parameters of Dirichlet distribution.

compare_alphas(n, alpha)

Arguments

n

number of weights which is generated from Dirichlet distribution

alpha

concentration parameter is given in vector form; each element represents each group.

Value

graphical display of different concentration parameters of Dirichlet distribution

Details

We assumed that the concentration parameters are identical in all weights, it means that \(\boldsymbol{\alpha} =[\alpha, \alpha, \cdots \alpha]\). The probability mass function of the weights is given by: $$\displaystyle{f(w_1,w_2, \cdots w_n;\boldsymbol{\alpha} )=\frac{\displaystyle{\Gamma(n\alpha)}} {{\Gamma(\alpha)}^n} \prod_{i=1}^{n}{w_i^{\alpha-1}}}$$ where \(\boldsymbol{\alpha} =[\alpha, \alpha, \cdots \alpha]\) is the vector of concentration parameters, and \(w_i\) is the stochastic weights which sum to one.

Examples

n <- 10000
alpha <- c(5,10,20)
compare_alphas(n,alpha)