AM_find_gamma_NegBin {AntMAN} | R Documentation |
Once the prior on the number of mixture components M is assumed to be a Negative Binomial with
parameter r>0
and 0<p<1
, with mean is 1+ r*p/(1-p), this function adopts a bisection method
to find the value of gamma
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 (Argiento and Iorio 2019).
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 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.
AM_find_gamma_NegBin( n, r, p, Kstar = 6, gam_min = 0.001, gam_max = 10000, tolerance = 0.1 )
n |
The sample size. |
r |
The dispersion parameter |
p |
The probability of failure parameter |
Kstar |
The mean number of clusters the user wants to specify. |
gam_min |
The lower bound of the interval in which |
gam_max |
The upper bound of the interval in which |
tolerance |
Level of tolerance of the method. |
A value of gamma
such that E(K)=K^{*}
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