tweedie in stan

How to choose M?

data {
  int <lower=1> N;     // Sample size
  int <lower=1> M;     // m ~ poison(lambda)
  real<lower=0> Y[N];  // outcome and each Yi=x1+x2+...+xm , and each xi ~ Gamma(alpha,gama) so Y|m ~ Gamma(m*alpha,gama)
}

parameters {
  real<lower=0> mu;
  real<lower=0> phi;
  real<lower=1, upper=2> p;
}

transformed parameters {
  real lambda = mu^(2-p)/(phi*(2-p));
  real alpha = (2-p)/(p-1);
  real gama = 1/phi*mu^(1-p)/(p-1);
}

model {
  mu ~ cauchy(0, 5);
  phi ~ cauchy(0, 5);

  for (n in 1:N) {
    if (Y[n] == 0) {
      target += -lambda;
    } else {
      vector[M] ps;
      for (m in 1:M)
        ps[m] = poisson_lpmf(m | lambda) + gamma_lpdf(Y[n] | m*alpha, gama);
        target += log_sum_exp(ps);

    }
  }
}

Should I consider “M” as a fixed value regarding to the data (like this codes) or it should be a random variable with Poisson distribution in the model? In each of the cases how should I write the codes? And how should I do this?
I appreciate any suggestion and help.
Thanks a lot.