# AM_find_gamma_Delta: Given that the prior on M is a dirac delta, find the gamma... In AntMAN: Anthology of Mixture Analysis Tools

## Description

Once a fixed value of the number of components M^* is specified, this function adopts a bisection method to find the value of γ such that the induced distribution on the number of clusters is centered around a user specifed value K^*, i.e. the function uses a bisection method to solve for γ \insertCiteargiento2019infinityAntMAN. The user can provide a lower γ_{l} and an upper γ_{u} bound for the possible values of γ. The default values are γ_l= 10^{-3} and γ_{u}=10. A default value for the tolerance is ε=0.1. Moreover, after a maximum number of iteration (default is 31), the function stops warning that convergence has not been reached.

## Usage

 ```1 2 3 4 5 6 7 8``` ```AM_find_gamma_Delta( n, Mstar, Kstar = 6, gam_min = 1e-04, gam_max = 10, tolerance = 0.1 ) ```

## Arguments

 `n` sample size. `Mstar` number of components of the mixture. `Kstar` mean number of clusters the user wants to specify. `gam_min` lower bound of the interval in which `gamma` should lie (default 1e-4). `gam_max` upper bound of the interval in which `gamma` should lie (default 10). `tolerance` Level of tolerance for the method.

## Value

A value of `gamma` such that E(K)=K^*

## Examples

 ```1 2 3 4 5``` ```n <- 82 Mstar <- 12 gam_de <- AM_find_gamma_Delta(n,Mstar,Kstar=6, gam_min=1e-4,gam_max=10, tolerance=0.1) prior_K_de <- AM_prior_K_Delta(n,gam_de,Mstar) prior_K_de%*%1:n ```

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