text: #ifndef STAN_MATH_PRIM_PROB_PARETO_LCDF_HPP
  #define STAN_MATH_PRIM_PROB_PARETO_LCDF_HPP
  
  #include <stan/math/prim/meta.hpp>
  #include <stan/math/prim/err.hpp>
  #include <stan/math/prim/fun/constants.hpp>
  #include <stan/math/prim/fun/exp.hpp>
  #include <stan/math/prim/fun/log.hpp>
  #include <stan/math/prim/fun/max_size.hpp>
  #include <stan/math/prim/fun/size.hpp>
  #include <stan/math/prim/fun/size_zero.hpp>
  #include <stan/math/prim/fun/value_of.hpp>
  #include <cmath>
  
  namespace stan {
  namespace math {
  
  template <typename T_y, typename T_scale, typename T_shape>
  return_type_t<T_y, T_scale, T_shape> pareto_lcdf(const T_y& y,
                                                   const T_scale& y_min,
                                                   const T_shape& alpha) {
    using T_partials_return = partials_return_t<T_y, T_scale, T_shape>;
    using std::exp;
    using std::log;
    static const char* function = "pareto_lcdf";
    check_not_nan(function, "Random variable", y);
    check_nonnegative(function, "Random variable", y);
    check_positive_finite(function, "Scale parameter", y_min);
    check_positive_finite(function, "Shape parameter", alpha);
    check_consistent_sizes(function, "Random variable", y, "Scale parameter",
                           y_min, "Shape parameter", alpha);
  
    if (size_zero(y, y_min, alpha)) {
      return 0;
    }
  
    T_partials_return P(0.0);
    operands_and_partials<T_y, T_scale, T_shape> ops_partials(y, y_min, alpha);
  
    scalar_seq_view<T_y> y_vec(y);
    scalar_seq_view<T_scale> y_min_vec(y_min);
    scalar_seq_view<T_shape> alpha_vec(alpha);
    size_t N = max_size(y, y_min, alpha);
  
    // Explicit return for extreme values
    // The gradients are technically ill-defined, but treated as zero
    for (size_t i = 0; i < stan::math::size(y); i++) {
      if (value_of(y_vec[i]) < value_of(y_min_vec[i])) {
        return ops_partials.build(negative_infinity());
      }
    }
  
    for (size_t n = 0; n < N; n++) {
      // Explicit results for extreme values
      // The gradients are technically ill-defined, but treated as zero
      if (value_of(y_vec[n]) == INFTY) {
        return ops_partials.build(0.0);
      }
  
      const T_partials_return log_dbl
          = log(value_of(y_min_vec[n]) / value_of(y_vec[n]));
      const T_partials_return y_min_inv_dbl = 1.0 / value_of(y_min_vec[n]);
      const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
  
      const T_partials_return Pn = 1.0 - exp(alpha_dbl * log_dbl);
  
      P += log(Pn);
  
      if (!is_constant_all<T_y>::value) {
        ops_partials.edge1_.partials_[n]
            += alpha_dbl * y_min_inv_dbl * exp((alpha_dbl + 1) * log_dbl) / Pn;
      }
      if (!is_constant_all<T_scale>::value) {
        ops_partials.edge2_.partials_[n]
            -= alpha_dbl * y_min_inv_dbl * exp(alpha_dbl * log_dbl) / Pn;
      }
      if (!is_constant_all<T_shape>::value) {
        ops_partials.edge3_.partials_[n]
            -= exp(alpha_dbl * log_dbl) * log_dbl / Pn;
      }
    }
    return ops_partials.build(P);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  