Stan Math Library  2.15.0
reverse mode automatic differentiation
pareto_lcdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_LCDF_HPP
3 
16 #include <boost/random/exponential_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 #include <limits>
20 
21 namespace stan {
22  namespace math {
23 
24  template <typename T_y, typename T_scale, typename T_shape>
26  pareto_lcdf(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
28  T_partials_return;
29 
30  if ( !( stan::length(y) && stan::length(y_min) && stan::length(alpha) ) )
31  return 0.0;
32 
33  static const char* function("pareto_lcdf");
34 
35  using std::log;
36  using std::exp;
37 
38  T_partials_return P(0.0);
39 
40  check_not_nan(function, "Random variable", y);
41  check_nonnegative(function, "Random variable", y);
42  check_positive_finite(function, "Scale parameter", y_min);
43  check_positive_finite(function, "Shape parameter", alpha);
44  check_consistent_sizes(function,
45  "Random variable", y,
46  "Scale parameter", y_min,
47  "Shape parameter", alpha);
48 
50  scalar_seq_view<const T_scale> y_min_vec(y_min);
51  scalar_seq_view<const T_shape> alpha_vec(alpha);
52  size_t N = max_size(y, y_min, alpha);
53 
55  operands_and_partials(y, y_min, alpha);
56 
57  // Explicit return for extreme values
58  // The gradients are technically ill-defined, but treated as zero
59  for (size_t i = 0; i < stan::length(y); i++) {
60  if (value_of(y_vec[i]) < value_of(y_min_vec[i]))
61  return operands_and_partials.value(negative_infinity());
62  }
63 
64  for (size_t n = 0; n < N; n++) {
65  // Explicit results for extreme values
66  // The gradients are technically ill-defined, but treated as zero
67  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
68  return operands_and_partials.value(0.0);
69  }
70 
71  const T_partials_return log_dbl = log(value_of(y_min_vec[n])
72  / value_of(y_vec[n]));
73  const T_partials_return y_min_inv_dbl = 1.0 / value_of(y_min_vec[n]);
74  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
75 
76  const T_partials_return Pn = 1.0 - exp(alpha_dbl * log_dbl);
77 
78  P += log(Pn);
79 
81  operands_and_partials.d_x1[n]
82  += alpha_dbl * y_min_inv_dbl * exp((alpha_dbl + 1) * log_dbl) / Pn;
84  operands_and_partials.d_x2[n]
85  -= alpha_dbl * y_min_inv_dbl * exp(alpha_dbl * log_dbl) / Pn;
87  operands_and_partials.d_x3[n]
88  -= exp(alpha_dbl * log_dbl) * log_dbl / Pn;
89  }
90  return operands_and_partials.value(P);
91  }
92 
93  }
94 }
95 #endif
VectorView< T_return_type, false, true > d_x2
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
return_type< T_y, T_scale, T_shape >::type pareto_lcdf(const T_y &y, const T_scale &y_min, const T_shape &alpha)
Definition: pareto_lcdf.hpp:26
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_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
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
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130

     [ Stan Home Page ] © 2011–2016, Stan Development Team.