AntMAN (version 1.1.0)

AM_prior_K_NegBin: computes the prior number of clusters

Description

This function computes the prior on the number of clusters, i.e. occupied component of the mixture for a Finite Dirichlet process when the prior on the component-weights of the mixture is a Dirichlet with parameter gamma (i.e. when unnormalized weights are distributed as Gamma(\(\gamma\),1)). This function can be used when the prior on the number of components is Negative Binomial with parameter \(r>0\) and \(0<p<1\), with mean \(mu =1+ r*p/(1-p)\). See argiento2019infinityAntMAN for more details.

Usage

AM_prior_K_NegBin(n, gamma, r, p)

Arguments

n

The sample size.

gamma

The gamma parameter of the Dirichlet distribution.

r

The dispersion parameter r of the Negative Binomial.

p

The probability of failure parameter p of the Negative Binomial.

Value

an AM_prior object, that is a vector of length n, reporting the values V(n,k) for k=1,...,n.

Details

There are no default values.

Examples

# NOT RUN {
n <- 50
gamma <- 1
r <- 0.1
p <- 0.91
gam_nb <- 0.2381641
prior_K_nb <-  AM_prior_K_NegBin(n,gam_nb,r,p)
plot(prior_K_nb)
# }