Stan Math Library  2.14.0
reverse mode automatic differentiation
frechet_lccdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_FRECHET_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_FRECHET_LCCDF_HPP
3 
4 #include <boost/random/weibull_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
23 #include <cmath>
24 
25 namespace stan {
26  namespace math {
27 
28  template <typename T_y, typename T_shape, typename T_scale>
30  frechet_lccdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
32  T_partials_return;
33 
34  static const char* function("frechet_lccdf");
35 
36  using boost::math::tools::promote_args;
37 
38  if (!(stan::length(y)
39  && stan::length(alpha)
40  && stan::length(sigma)))
41  return 0.0;
42 
43  T_partials_return ccdf_log(0.0);
44  check_positive(function, "Random variable", y);
45  check_positive_finite(function, "Shape parameter", alpha);
46  check_positive_finite(function, "Scale parameter", sigma);
47 
49  operands_and_partials(y, alpha, sigma);
50 
51  using std::log;
52  using std::exp;
53  VectorView<const T_y> y_vec(y);
54  VectorView<const T_scale> sigma_vec(sigma);
55  VectorView<const T_shape> alpha_vec(alpha);
56  size_t N = max_size(y, sigma, alpha);
57 
58  for (size_t n = 0; n < N; n++) {
59  const T_partials_return y_dbl = value_of(y_vec[n]);
60  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
61  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
62  const T_partials_return pow_ = pow(sigma_dbl / y_dbl, alpha_dbl);
63  const T_partials_return exp_ = exp(-pow_);
64 
65  ccdf_log += log1m(exp_);
66 
67  const T_partials_return rep_deriv_ = pow_ / (1.0 / exp_ - 1);
69  operands_and_partials.d_x1[n] -= alpha_dbl / y_dbl * rep_deriv_;
71  operands_and_partials.d_x2[n] -= log(y_dbl / sigma_dbl) * rep_deriv_;
73  operands_and_partials.d_x3[n] += alpha_dbl / sigma_dbl * rep_deriv_;
74  }
75  return operands_and_partials.value(ccdf_log);
76  }
77 
78  }
79 }
80 #endif
VectorView< T_return_type, false, true > d_x2
return_type< T_y, T_shape, T_scale >::type frechet_lccdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:13
VectorView< T_return_type, false, true > d_x1

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