Integrate_1d not finding integrand function

Modeling
1

Integrate_1d is not finding my integrand function. I am receving the error

variable "integrand" does not exist.

My Stan code is shown below.

functions {
  real sev_logpdf(real y, real mu, real sigma){
    real z;
    z = (y - mu) / sigma;
    return -log(sigma) + z - exp(z);
  }
  
  real sev_logccdf(real y, real mu, real sigma){
    return -exp((y - mu) / sigma);
  }
  
  real sev_logcdf(real y, real mu, real sigma){
    return log1m_exp(-exp((y - mu) / sigma));
  }
  real integrand(real x,       
            real xc,      
            real[] theta, 
            real[] x_r,   
            int[] x_i) { 
                      
    //real mu1 = theta[1];
    //real sigma1 = theta[2];
    //real mu2 = theta[3];
    //real sigma2 = theta[4];
    real mu3 = theta[1];
    real sigma3 = theta[2];
    //real log_pi = theta[7];
    
    real z = (1/sigma3)*x^(1/sigma3-1)*exp(-x^(1/sigma3)*exp(-mu3/sigma3)-mu3/sigma3);
    
    return z;
    }
}
data {
  int N_obs;
  int N_cens;
  real endtime_obs[N_obs];
  real endtime_cens[N_cens];
  real starttime_obs[N_obs];
  real starttime_cens[N_cens];
  vector<lower=0, upper=1>[2] p; # quantiles to model
  int N_obs_s5;
  int N_cens_s5;
  real endtime_obs_s5[N_obs_s5];
  real endtime_cens_s5[N_cens_s5];
  real starttime_obs_s5[N_obs_s5];
  real starttime_cens_s5[N_cens_s5];
}
transformed data{
  vector[2] z_corr;
  for(i in 1:2)
    z_corr[i] = log(-1.0 * log1m(p[i])); # used to get location(mu) from quantile(t_p)
}
parameters{
  real log_tp1;
  real log_tp2;
  real<lower=0> sigma1;
  real<lower=0, upper=1> sigma2;
  real logit_pi;
  real<lower = 0> mu3;
  real<lower = 0> sigma3;
}
transformed parameters{
  real mu1;
  real mu2;
  real log_pi;
  mu1 = log_tp1 - (sigma1 * z_corr[1]); //change
  mu2 = log_tp2 - (sigma2 * z_corr[2]);
  log_pi = log_inv_logit(logit_pi);
}
model{
  real tmp[2];
  for(i in 1:N_obs){
    tmp[1] = log_sum_exp(log_pi + sev_logpdf(endtime_obs[i], mu1, sigma1) +
                           sev_logccdf(endtime_obs[i], mu2, sigma2),
                         sev_logpdf( endtime_obs[i], mu2, sigma2) + 
                           log1m_exp(log_pi + sev_logcdf(endtime_obs[i], mu1, sigma1)
                           )
    );
    tmp[2] = log1m_exp(log_pi + sev_logcdf(starttime_obs[i], mu1, sigma1)) + 
      sev_logccdf(starttime_obs[i], mu2, sigma2);
    
    target += tmp[1] - tmp[2];
  }

  for(i in 1:N_cens){
    tmp[1] = log1m_exp(log_pi + sev_logcdf(endtime_cens[i], mu1, sigma1)) + 
      sev_logccdf(endtime_cens[i], mu2, sigma2);
    tmp[2] = log1m_exp(log_pi + sev_logcdf(starttime_cens[i], mu1, sigma1)) + 
      sev_logccdf(starttime_cens[i], mu2, sigma2);
    target += tmp[1] - tmp[2];
  }
  for(i in 1:N_obs_s5){
    tmp[1] = sev_logpdf(endtime_obs_s5[i], mu3, sigma3);
    tmp[2] = sev_logccdf(starttime_obs_s5[i], mu3, sigma3);
    target += tmp[1]- tmp[2];
  }
  for(i in 1:N_cens_s5){
    tmp[1] = sev_logccdf(endtime_cens_s5[i], mu3, sigma3);
    tmp[2] = sev_logccdf(starttime_cens_s5[i], mu3, sigma3);
    target += tmp[1] - tmp[2];
  }
  //priors
  log_tp1 ~ normal(8, 4);
  log_tp2 ~ normal(10, 4);
  sigma1 ~ lognormal(0, 2.5);
  sigma2 ~ lognormal(0, 2.5);
  sigma3 ~ lognormal(0, 2.5);
  logit_pi ~ normal(-3,2);
  mu3 ~ normal(0,10);
}
generated quantities {
  real<lower = 0> Fs5;
  Fs5 = integrate_1d(integrand, 
                     0, 
                     1000,
                     {mu3,sigma3},
                     x_r,
                     x_i,
                     1e-8);
}

Can anyone see the mistake that I am making?

PS the integral can be solved analytically. I am just checking how the function works.

Edit: I bet I have an outdated version of Stan that does not support integrate_1d.
Edit: I am using Stan version 2.18. My understanding is that integrate_1d should work for this version of Stan.

2

From looking at the docs, the integrate_1d function wasn’t introduced until 2.19. So you would need to upgrade unfortunately

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