compare_alphas: Graphical display to investigate the impact of concentration...

In Mayooran1987/mixingsimulation: Microbiological Risk Assessment of Powder Mixing Process by Simulation Results

Graphical display to investigate the impact of concentration parameter values in the Dirichlet distribution.

Description

This function provides a graphical display to investigate the impact of concentration parameter values in the Dirichlet distribution.

Usage

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.

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 parameter, and w_i is the stochastic weights which sum to one.

Value

graphical display of different concentration parameters of Dirichlet distribution

Examples

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

Mayooran1987/mixingsimulation documentation built on May 12, 2023, 12:36 a.m.