Hypergeometic programming

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I’m trying to program a simple Lincoln-Peterson mark-recapture example using the hyperG likelihood:
I have easily programmed this example using the more common binomial likelihood, but also want and need to be able to program using the HyperG. I forgot to add that this appears to compile, but when I run it sampling does not occur because ‘b’ takes a values on the order of negative 200000 despite being constrained to no less than 70.

Here are my Rstan and stan files:
//HG1.stan. Test of simple Lincoln-Peterson model using a hypergeometric likelihood
//February 13 2019

data{
int<lower = 0> a;//M
int<lower=0> N; //C
int<lower = 0, upper = min(a,N)> n;//R
}

transformed data{
int<lower = N-n> b; //N-M
}

//parameters{
// real<lower = (N-n)> b; //(C-R+M)> N;
// }

model {
// R~binomial(C, M/N);
n~hypergeometric(N,a,b); //n, N and a known; b is unkown and to be estimated
}

generated quantities{
int <lower = 0>Pop;
Pop = a+b; //total population size
}

#HG1_stan.R
#Test: Simple Lincoln-Peterson mark-recp model using a hypergeomtric likelihood
#February 13 2019

#a = 500; #number marked and released
#N =100; #number recaptured
#n = 30; #number marked among the C recaptures

stanDat <- list(a = 500, N = 100, n = 30)

#sample posterior:
HG1fit <- stan(file=“HG1.stan”, data = stanDat, init=list(list(b = 80)),iter = 100, chains = 1)

print(HG1fit)

The right-most remmed-out notations in the .stan file are the corresponding variables in the mark-recap examples in Section 15.3, pp. 2016-17 of the Stan Reference Manual.