text: #ifndef STAN_MATH_PRIM_SCAL_PROB_GUMBEL_CDF_HPP
  #define STAN_MATH_PRIM_SCAL_PROB_GUMBEL_CDF_HPP
  
  #include <stan/math/prim/meta.hpp>
  #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
  #include <stan/math/prim/scal/err/check_finite.hpp>
  #include <stan/math/prim/scal/err/check_not_nan.hpp>
  #include <stan/math/prim/scal/err/check_positive.hpp>
  #include <stan/math/prim/scal/fun/size_zero.hpp>
  #include <stan/math/prim/scal/fun/value_of.hpp>
  #include <cmath>
  
  namespace stan {
  namespace math {
  
  /** \ingroup prob_dists
   * Returns the Gumbel distribution cumulative distribution for the given
   * location and scale. Given containers of matching sizes, returns the
   * product of probabilities.
   *
   * @tparam T_y type of real parameter
   * @tparam T_loc type of location parameter
   * @tparam T_scale type of scale parameter
   * @param y real parameter
   * @param mu location parameter
   * @param beta scale parameter
   * @return probability or product of probabilities
   * @throw std::domain_error if y is nan, mu is infinite, or beta is nonpositive
   * @throw std::invalid_argument if container sizes mismatch
   */
  template <typename T_y, typename T_loc, typename T_scale>
  return_type_t<T_y, T_loc, T_scale> gumbel_cdf(const T_y& y, const T_loc& mu,
                                                const T_scale& beta) {
    static const char* function = "gumbel_cdf";
    using T_partials_return = partials_return_t<T_y, T_loc, T_scale>;
  
    using std::exp;
  
    T_partials_return cdf(1.0);
    if (size_zero(y, mu, beta)) {
      return cdf;
    }
  
    check_not_nan(function, "Random variable", y);
    check_finite(function, "Location parameter", mu);
    check_not_nan(function, "Scale parameter", beta);
    check_positive(function, "Scale parameter", beta);
    check_consistent_sizes(function, "Random variable", y, "Location parameter",
                           mu, "Scale parameter", beta);
  
    operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, beta);
  
    scalar_seq_view<T_y> y_vec(y);
    scalar_seq_view<T_loc> mu_vec(mu);
    scalar_seq_view<T_scale> beta_vec(beta);
    size_t N = max_size(y, mu, beta);
  
    for (size_t n = 0; n < N; n++) {
      const T_partials_return y_dbl = value_of(y_vec[n]);
      const T_partials_return mu_dbl = value_of(mu_vec[n]);
      const T_partials_return beta_dbl = value_of(beta_vec[n]);
      const T_partials_return scaled_diff = (y_dbl - mu_dbl) / beta_dbl;
      const T_partials_return rep_deriv
          = exp(-scaled_diff - exp(-scaled_diff)) / beta_dbl;
      const T_partials_return cdf_ = exp(-exp(-scaled_diff));
      cdf *= cdf_;
  
      if (!is_constant_all<T_y>::value) {
        ops_partials.edge1_.partials_[n] += rep_deriv / cdf_;
      }
      if (!is_constant_all<T_loc>::value) {
        ops_partials.edge2_.partials_[n] -= rep_deriv / cdf_;
      }
      if (!is_constant_all<T_scale>::value) {
        ops_partials.edge3_.partials_[n] -= rep_deriv * scaled_diff / cdf_;
      }
    }
  
    if (!is_constant_all<T_y>::value) {
      for (size_t n = 0; n < stan::length(y); ++n) {
        ops_partials.edge1_.partials_[n] *= cdf;
      }
    }
    if (!is_constant_all<T_loc>::value) {
      for (size_t n = 0; n < stan::length(mu); ++n) {
        ops_partials.edge2_.partials_[n] *= cdf;
      }
    }
    if (!is_constant_all<T_scale>::value) {
      for (size_t n = 0; n < stan::length(beta); ++n) {
        ops_partials.edge3_.partials_[n] *= cdf;
      }
    }
    return ops_partials.build(cdf);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  