# AM_find_gamma_NegBin: Once the prior on the numbuer of mixture \$M\$ is assumed to be... In AntMAN: Anthology of Mixture Analysis Tools

## Description

Once the prior on the numbuer of mixture \$M\$ is assumed to be a Negative Binomial Negative Binomial with parameter `r>0` and `0<p<1`, with mean is 1+ r*p/(1-p), this function adopt a bisection method to find the value of `gamma` such that the induced distribution on the number of clusers is centered around a user specifed value K^*, i.e. the function use a bisection method to solve Eq.~eq:findgamma of WE NEED TO CITE ANTMAN PAPER. The user can provide a lower γ_{l} and an upper γ_{u} bound for the possible values of \$gamma\$. The default values are γ_l= 10^{-3} and γ_{u}=10. A defaault 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 bee reached.

## Usage

 ```1 2``` ```AM_find_gamma_NegBin(n, r, p, Kstar = 6, gam_min = 0.001, gam_max = 10000, tolerance = 0.1) ```

## Arguments

 `n` The sample size `r` The dispersion parameter `r` of Negative Binomial `p` The probability of failure parameter `p` of Negative Binomial `Kstar` The mean number of cluster the user want to specify `gam_min` The lower bound of the interval in which `gamma` should be lie `gam_max` The upper bound of the interval in which `gamma` should lie `tolerance` tolerance of the method

## Value

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

## Examples

 ```1 2 3 4 5 6``` ```n <- 82 r <- 1 p <- 0.8571 gam_nb= AM_find_gamma_NegBin(n,r,p,Kstar=6, gam_min=0.001,gam_max=10000, tolerance=0.1) prior_K_nb= AM_prior_K_NegBin(n,gam_nb, r, p) prior_K_nb%*%1:n ```

AntMAN documentation built on Oct. 30, 2019, 11:24 a.m.