# AM_prior_K_NegBin: computes the prior number of clusters In AntMAN: Anthology of Mixture Analysis Tools

## 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(γ,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 \insertCiteargiento2019infinityAntMAN for more details.

## Usage

 `1` ```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.

## Details

There are no default values.

## Value

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

## Examples

 ```1 2 3 4 5 6 7``` ```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) ```

AntMAN documentation built on July 23, 2021, 5:08 p.m.