text: #ifndef STAN_MATH_PRIM_PROB_EXP_MOD_NORMAL_LPDF_HPP
  #define STAN_MATH_PRIM_PROB_EXP_MOD_NORMAL_LPDF_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/erfc.hpp>
  #include <stan/math/prim/fun/exp.hpp>
  #include <stan/math/prim/fun/inv.hpp>
  #include <stan/math/prim/fun/log.hpp>
  #include <stan/math/prim/fun/max_size.hpp>
  #include <stan/math/prim/fun/size_zero.hpp>
  #include <stan/math/prim/fun/square.hpp>
  #include <stan/math/prim/fun/to_ref.hpp>
  #include <stan/math/prim/fun/value_of.hpp>
  #include <stan/math/prim/functor/operands_and_partials.hpp>
  #include <cmath>
  
  namespace stan {
  namespace math {
  
  template <bool propto, typename T_y, typename T_loc, typename T_scale,
            typename T_inv_scale,
            require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
                T_y, T_loc, T_scale, T_inv_scale>* = nullptr>
  return_type_t<T_y, T_loc, T_scale, T_inv_scale> exp_mod_normal_lpdf(
      const T_y& y, const T_loc& mu, const T_scale& sigma,
      const T_inv_scale& lambda) {
    using T_partials_return = partials_return_t<T_y, T_loc, T_scale, T_inv_scale>;
    using T_y_ref = ref_type_if_t<!is_constant<T_y>::value, T_y>;
    using T_mu_ref = ref_type_if_t<!is_constant<T_loc>::value, T_loc>;
    using T_sigma_ref = ref_type_if_t<!is_constant<T_scale>::value, T_scale>;
    using T_lambda_ref
        = ref_type_if_t<!is_constant<T_inv_scale>::value, T_inv_scale>;
    static const char* function = "exp_mod_normal_lpdf";
    check_consistent_sizes(function, "Random variable", y, "Location parameter",
                           mu, "Scale parameter", sigma, "Inv_scale paramter",
                           lambda);
    T_y_ref y_ref = y;
    T_mu_ref mu_ref = mu;
    T_sigma_ref sigma_ref = sigma;
    T_lambda_ref lambda_ref = lambda;
  
    const auto& y_col = as_column_vector_or_scalar(y_ref);
    const auto& mu_col = as_column_vector_or_scalar(mu_ref);
    const auto& sigma_col = as_column_vector_or_scalar(sigma_ref);
    const auto& lambda_col = as_column_vector_or_scalar(lambda_ref);
  
    const auto& y_arr = as_array_or_scalar(y_col);
    const auto& mu_arr = as_array_or_scalar(mu_col);
    const auto& sigma_arr = as_array_or_scalar(sigma_col);
    const auto& lambda_arr = as_array_or_scalar(lambda_col);
  
    ref_type_t<decltype(value_of(y_arr))> y_val = value_of(y_arr);
    ref_type_t<decltype(value_of(mu_arr))> mu_val = value_of(mu_arr);
    ref_type_t<decltype(value_of(sigma_arr))> sigma_val = value_of(sigma_arr);
    ref_type_t<decltype(value_of(lambda_arr))> lambda_val = value_of(lambda_arr);
  
    check_not_nan(function, "Random variable", y_val);
    check_finite(function, "Location parameter", mu_val);
    check_positive_finite(function, "Scale parameter", sigma_val);
    check_positive_finite(function, "Inv_scale parameter", lambda_val);
  
    if (size_zero(y, mu, sigma, lambda)) {
      return 0.0;
    }
    if (!include_summand<propto, T_y, T_loc, T_scale, T_inv_scale>::value) {
      return 0.0;
    }
  
    const auto& inv_sigma
        = to_ref_if<!is_constant_all<T_y, T_loc>::value>(inv(sigma_val));
    const auto& sigma_sq
        = to_ref_if<!is_constant_all<T_scale>::value>(square(sigma_val));
    const auto& lambda_sigma_sq = to_ref(lambda_val * sigma_sq);
    const auto& mu_minus_y = to_ref(mu_val - y_val);
    const auto& inner_term
        = to_ref_if<!is_constant_all<T_y, T_loc, T_scale, T_inv_scale>::value>(
            (mu_minus_y + lambda_sigma_sq) * INV_SQRT_TWO * inv_sigma);
    const auto& erfc_calc = to_ref(erfc(inner_term));
  
    size_t N = max_size(y, mu, sigma, lambda);
    T_partials_return logp(0.0);
    if (include_summand<propto>::value) {
      logp -= LOG_TWO * N;
    }
    if (include_summand<propto, T_inv_scale>::value) {
      logp += sum(log(lambda_val)) * N / size(lambda);
    }
    const auto& log_erfc_calc = log(erfc_calc);
    logp
        += sum(lambda_val * (mu_minus_y + 0.5 * lambda_sigma_sq) + log_erfc_calc);
  
    operands_and_partials<T_y_ref, T_mu_ref, T_sigma_ref, T_lambda_ref>
        ops_partials(y_ref, mu_ref, sigma_ref, lambda_ref);
    if (!is_constant_all<T_y, T_loc, T_scale, T_inv_scale>::value) {
      const auto& exp_m_sq_inner_term = exp(-square(inner_term));
      const auto& deriv_logerfc = to_ref_if<
          !is_constant_all<T_y, T_loc>::value + !is_constant_all<T_scale>::value
              + !is_constant_all<T_inv_scale>::value
          >= 2>(-SQRT_TWO_OVER_SQRT_PI * exp_m_sq_inner_term / erfc_calc);
      if (!is_constant_all<T_y, T_loc>::value) {
        const auto& deriv = to_ref_if < !is_constant_all<T_y>::value
                            && !is_constant_all<T_loc>::value
                                   > (lambda_val + deriv_logerfc * inv_sigma);
        if (!is_constant_all<T_y>::value) {
          ops_partials.edge1_.partials_ = -deriv;
        }
        if (!is_constant_all<T_loc>::value) {
          ops_partials.edge2_.partials_ = deriv;
        }
      }
      if (!is_constant_all<T_scale>::value) {
        ops_partials.edge3_.partials_
            = sigma_val * square(lambda_val)
              + deriv_logerfc * (lambda_val - mu_minus_y / sigma_sq);
      }
      if (!is_constant_all<T_inv_scale>::value) {
        ops_partials.edge4_.partials_ = inv(lambda_val) + lambda_sigma_sq
                                        + mu_minus_y + deriv_logerfc * sigma_val;
      }
    }
  
    return ops_partials.build(logp);
  }
  
  template <typename T_y, typename T_loc, typename T_scale, typename T_inv_scale>
  inline return_type_t<T_y, T_loc, T_scale, T_inv_scale> exp_mod_normal_lpdf(
      const T_y& y, const T_loc& mu, const T_scale& sigma,
      const T_inv_scale& lambda) {
    return exp_mod_normal_lpdf<false>(y, mu, sigma, lambda);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  