text: // Arguments: Ints, Ints, Doubles
  #include <stan/math/prim.hpp>
  #include <boost/math/special_functions/binomial.hpp>
  
  using stan::math::var;
  using std::numeric_limits;
  using std::vector;
  
  class AgradCdfBinomial : public AgradCdfTest {
   public:
    void valid_values(vector<vector<double> >& parameters, vector<double>& cdf) {
      vector<double> param(3);
  
      param[0] = 17;   // Successes
      param[1] = 45;   // Trials
      param[2] = 0.5;  // Probability
      parameters.push_back(param);
      cdf.push_back(0.06757822542283530020679);  // expected cdf
    }
  
    void invalid_values(vector<size_t>& index, vector<double>& value) {
      // N (Trials)
      index.push_back(1U);
      value.push_back(-1);
  
      // p (Probability
      index.push_back(2U);
      value.push_back(-1e-4);
  
      index.push_back(2U);
      value.push_back(1 + 1e-4);
    }
  
    bool has_lower_bound() { return false; }
  
    bool has_upper_bound() { return false; }
  
    template <typename T_n, typename T_N, typename T_prob, typename T3,
              typename T4, typename T5>
    stan::return_type_t<T_prob> cdf(const T_n& n, const T_N& N,
                                    const T_prob& theta, const T3&, const T4&,
                                    const T5&) {
      return stan::math::binomial_cdf(n, N, theta);
    }
  
    template <typename T_n, typename T_N, typename T_prob, typename T3,
              typename T4, typename T5>
    stan::return_type_t<T_prob> cdf_function(const T_n& n, const T_N& N,
                                             const T_prob& theta, const T3&,
                                             const T4&, const T5&) {
      using boost::math::binomial_coefficient;
      using std::exp;
      using std::log;
  
      stan::return_type_t<T_prob> cdf(0);
  
      for (int i = 0; i <= n; i++) {
        cdf += binomial_coefficient<double>(N, i)
               * exp(i * log(theta) + (N - i) * log(1 - theta));
      }
  
      return cdf;
    }
  };
  