AM_prior_K_Pois {AntMAN}

Computes the prior number of clusters

Description

This function computes the prior on the number of clusters, i.e. occupied components 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 Shifted Poisson of parameter Lambda. See (Argiento and Iorio 2019) for more details.

Usage

AM_prior_K_Pois(n, gamma, Lambda)

Arguments

n

The sample size.

gamma

The gamma parameter of the Dirichlet distribution.

Lambda

The Lambda parameter of the Poisson.

Details

There are no default values.

Value

an AM_prior object, that is a vector of length n, reporting the values of the prior on the number of clusters induced by the prior on M and w, i.e. p^*_k for k=1,...,n. See (Argiento and Iorio 2019) for more details.

Examples

n <- 82
Lambda <- 10
gam_po <- 0.1550195
prior_K_po <-  AM_prior_K_Pois(n,gam_po,Lambda)
plot(prior_K_po)