exp_mod_normal_lccdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_EXP_MOD_NORMAL_LCCDF_HPP
#define STAN_MATH_PRIM_PROB_EXP_MOD_NORMAL_LCCDF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/as_column_vector_or_scalar.hpp>
#include <stan/math/prim/fun/as_array_or_scalar.hpp>
#include <stan/math/prim/fun/as_value_column_array_or_scalar.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/erf.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/inv.hpp>
#include <stan/math/prim/fun/is_inf.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/scalar_seq_view.hpp>
#include <stan/math/prim/fun/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/partials_propagator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <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>
inline return_type_t<T_y, T_loc, T_scale, T_inv_scale> exp_mod_normal_lccdf(
    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_not_constant_t<T_y>;
  using T_mu_ref = ref_type_if_not_constant_t<T_loc>;
  using T_sigma_ref = ref_type_if_not_constant_t<T_scale>;
  using T_lambda_ref = ref_type_if_not_constant_t<T_inv_scale>;
  static constexpr const char* function = "exp_mod_normal_lccdf";
  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;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) mu_val = to_ref(as_value_column_array_or_scalar(mu_ref));
  decltype(auto) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
  decltype(auto) lambda_val
      = to_ref(as_value_column_array_or_scalar(lambda_ref));
 
  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;
  }
 
  auto ops_partials
      = make_partials_propagator(y_ref, mu_ref, sigma_ref, lambda_ref);
 
  scalar_seq_view<decltype(y_val)> y_vec(y_val);
  for (size_t n = 0, size_y = stan::math::size(y); n < size_y; n++) {
    if (is_inf(y_vec[n])) {
      return ops_partials.build(y_vec[n] > 0 ? negative_infinity() : 0);
    }
  }
 
  const auto& inv_sigma
      = to_ref_if<is_any_autodiff_v<T_y, T_loc, T_scale>>(inv(sigma_val));
  const auto& diff = to_ref(y_val - mu_val);
  const auto& v = to_ref(lambda_val * sigma_val);
  const auto& scaled_diff = to_ref(diff * INV_SQRT_TWO * inv_sigma);
  const auto& scaled_diff_diff
      = to_ref_if<is_any_autodiff_v<T_y, T_loc, T_scale, T_inv_scale>>(
          scaled_diff - v * INV_SQRT_TWO);
  const auto& erf_calc = to_ref(0.5 * (1 + erf(scaled_diff_diff)));
 
  const auto& exp_term
      = to_ref_if<is_any_autodiff_v<T_y, T_loc, T_scale, T_inv_scale>>(
          exp(0.5 * square(v) - lambda_val * diff));
  const auto& ccdf_n
      = to_ref(0.5 - 0.5 * erf(scaled_diff) + exp_term * erf_calc);
 
  T_partials_return ccdf_log = sum(log(ccdf_n));
 
  if constexpr (is_any_autodiff_v<T_y, T_loc, T_scale, T_inv_scale>) {
    const auto& exp_term_2 = to_ref_if<(
        is_any_autodiff_v<T_y, T_loc, T_scale> && is_autodiff_v<T_inv_scale>)>(
        exp(-square(scaled_diff_diff)));
    if constexpr (is_any_autodiff_v<T_y, T_loc, T_scale>) {
      constexpr bool need_deriv_refs
          = is_any_autodiff_v<T_y, T_loc> && is_autodiff_v<T_scale>;
      const auto& deriv_1
          = to_ref_if<need_deriv_refs>(lambda_val * exp_term * erf_calc);
      const auto& deriv_2 = to_ref_if<need_deriv_refs>(
          INV_SQRT_TWO_PI * exp_term * exp_term_2 * inv_sigma);
      const auto& sq_scaled_diff = square(scaled_diff);
      const auto& exp_m_sq_scaled_diff = exp(-sq_scaled_diff);
      const auto& deriv_3 = to_ref_if<need_deriv_refs>(
          INV_SQRT_TWO_PI * exp_m_sq_scaled_diff * inv_sigma);
      if constexpr (is_any_autodiff_v<T_y, T_loc>) {
        const auto& deriv
            = to_ref_if<(is_autodiff_v<T_loc> && is_autodiff_v<T_y>)>(
                (deriv_1 - deriv_2 + deriv_3) / ccdf_n);
        if constexpr (is_autodiff_v<T_y>) {
          partials<0>(ops_partials) = -deriv;
        }
        if constexpr (is_autodiff_v<T_loc>) {
          partials<1>(ops_partials) = deriv;
        }
      }
      if constexpr (is_autodiff_v<T_scale>) {
        edge<2>(ops_partials).partials_
            = ((deriv_1 - deriv_2) * v
               + (deriv_3 - deriv_2) * scaled_diff * SQRT_TWO)
              / ccdf_n;
      }
    }
    if constexpr (is_autodiff_v<T_inv_scale>) {
      edge<3>(ops_partials).partials_
          = exp_term
            * ((v * sigma_val - diff) * erf_calc
               - INV_SQRT_TWO_PI * sigma_val * exp_term_2)
            / ccdf_n;
    }
  }
 
  return ops_partials.build(ccdf_log);
}
 
}  // namespace math
}  // namespace stan
#endif