Unconstrained quantile to truncated normal conversion

truncnorm_ng.stan

functions {
  // lower bound is a, upper bound is b, rv is x, mean is mu, sd is sigma
  vector xi(vector x, real mu, real sigma) {
    return((x - mu)./sigma);
  }
  real alpha(real a, real mu, real sigma) {
    real out;
    out = (a==negative_infinity())? negative_infinity(): (a - mu)/sigma;
    return(out);
  }
  real beta(real b, real mu, real sigma) {
    real out;
    out = (b==positive_infinity())? positive_infinity(): (b - mu)/sigma;
    return(out);
  }
  real Z(real a, real b, real mu, real sigma) {
    return(normal_cdf(beta(b, mu, sigma), 0.0, 1.0) - normal_cdf(alpha(a, mu, sigma), 0.0, 1.0));
  }
  
  // converts a vector of inverse quantiles (a CDF) to the corresponding quantile of 
  // a truncated normal distribution in [a, b] with location = location and scale = scale. 
  // convenient for 
  vector truncnorm_ng(vector p, // vector the cdf of some random variable
                      real a, // lower bound, can be negative_infinity() and positive_infinity()
                      real b, // upper bound, can be negative_infinity() and positive_infinity()
                      real location, // location and scale are self explanatory
                      real scale) {
    vector[rows(p)] out;
    real tmp_Z;
    real tmp_alpha;
    
    tmp_alpha = normal_cdf(alpha(a, location, scale), 0, 1);
    tmp_Z = normal_cdf(beta(b, location, scale), 0, 1) - tmp_alpha;
    for(i in 1:rows(p)) {
      out[i] = inv_Phi(tmp_alpha + p[i]*tmp_Z)*scale + location;
    }
    return(out);
  }
}
model {
  
}