weibull_lccdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_WEIBULL_LCCDF_HPP
#define STAN_MATH_PRIM_PROB_WEIBULL_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/log.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/max_size.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_shape, typename T_scale,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_shape, T_scale>* = nullptr>
inline return_type_t<T_y, T_shape, T_scale> weibull_lccdf(
    const T_y& y, const T_shape& alpha, const T_scale& sigma) {
  using T_partials_return = partials_return_t<T_y, T_shape, T_scale>;
  using T_y_ref = ref_type_if_not_constant_t<T_y>;
  using T_alpha_ref = ref_type_if_not_constant_t<T_shape>;
  using T_sigma_ref = ref_type_if_not_constant_t<T_scale>;
  using std::pow;
  static constexpr const char* function = "weibull_lccdf";
 
  T_y_ref y_ref = y;
  T_alpha_ref alpha_ref = alpha;
  T_sigma_ref sigma_ref = sigma;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) alpha_val = to_ref(as_value_column_array_or_scalar(alpha_ref));
  decltype(auto) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
 
  check_nonnegative(function, "Random variable", y_val);
  check_positive_finite(function, "Shape parameter", alpha_val);
  check_positive_finite(function, "Scale parameter", sigma_val);
 
  if (size_zero(y, alpha, sigma)) {
    return 0.0;
  }
 
  auto ops_partials = make_partials_propagator(y_ref, alpha_ref, sigma_ref);
 
  const auto& pow_n = to_ref_if<is_any_autodiff_v<T_y, T_shape, T_scale>>(
      pow(y_val / sigma_val, alpha_val));
  T_partials_return ccdf_log = -sum(pow_n);
 
  if constexpr (is_autodiff_v<T_y>) {
    partials<0>(ops_partials) = -alpha_val / y_val * pow_n;
  }
  if constexpr (is_autodiff_v<T_shape>) {
    partials<1>(ops_partials) = -log(y_val / sigma_val) * pow_n;
  }
  if constexpr (is_autodiff_v<T_scale>) {
    partials<2>(ops_partials) = alpha_val / sigma_val * pow_n;
  }
  return ops_partials.build(ccdf_log);
}
 
}  // namespace math
}  // namespace stan
#endif