frechet_lccdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_FRECHET_LCCDF_HPP
#define STAN_MATH_PRIM_PROB_FRECHET_LCCDF_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/log1m.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/multiply_log.hpp>
#include <stan/math/prim/fun/pow.hpp>
#include <stan/math/prim/fun/scalar_seq_view.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/fun/value_of.hpp>
#include <boost/random/weibull_distribution.hpp>
#include <boost/random/variate_generator.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> frechet_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_t<T_y>;
  using T_alpha_ref = ref_type_t<T_shape>;
  using T_sigma_ref = ref_type_t<T_scale>;
  static constexpr const char* function = "frechet_lccdf";
  T_y_ref y_ref = y;
  T_alpha_ref alpha_ref = alpha;
  T_sigma_ref sigma_ref = sigma;
  using std::pow;
  check_positive(function, "Random variable", y_ref);
  check_positive_finite(function, "Shape parameter", alpha_ref);
  check_positive_finite(function, "Scale parameter", sigma_ref);
 
  if (size_zero(y_ref, alpha_ref, sigma_ref)) {
    return 0;
  }
 
  T_partials_return ccdf_log(0.0);
  auto ops_partials = make_partials_propagator(y_ref, alpha_ref, sigma_ref);
 
  scalar_seq_view<T_y> y_vec(y_ref);
  scalar_seq_view<T_scale> sigma_vec(sigma_ref);
  scalar_seq_view<T_shape> alpha_vec(alpha_ref);
  size_t N = max_size(y_ref, sigma_ref, alpha_ref);
 
  for (size_t n = 0; n < N; n++) {
    const T_partials_return y_dbl = y_vec.val(n);
    const T_partials_return sigma_dbl = sigma_vec.val(n);
    const T_partials_return alpha_dbl = alpha_vec.val(n);
    const T_partials_return pow_n = pow(sigma_dbl / y_dbl, alpha_dbl);
    const T_partials_return exp_n = exp(-pow_n);
 
    ccdf_log += log1m(exp_n);
 
    const T_partials_return rep_deriv = pow_n / (1.0 / exp_n - 1);
    if constexpr (is_autodiff_v<T_y>) {
      partials<0>(ops_partials)[n] -= alpha_dbl / y_dbl * rep_deriv;
    }
    if constexpr (is_autodiff_v<T_shape>) {
      partials<1>(ops_partials)[n] -= log(y_dbl / sigma_dbl) * rep_deriv;
    }
    if constexpr (is_autodiff_v<T_scale>) {
      partials<2>(ops_partials)[n] += alpha_dbl / sigma_dbl * rep_deriv;
    }
  }
  return ops_partials.build(ccdf_log);
}
 
}  // namespace math
}  // namespace stan
#endif