Stan Math Library  2.15.0
reverse mode automatic differentiation
pareto_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_LPDF_HPP
3 
19 #include <boost/random/exponential_distribution.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 
23 namespace stan {
24  namespace math {
25 
26  // Pareto(y|y_m, alpha) [y > y_m; y_m > 0; alpha > 0]
27  template <bool propto,
28  typename T_y, typename T_scale, typename T_shape>
30  pareto_lpdf(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
31  static const char* function("pareto_lpdf");
33  T_partials_return;
34 
35  using std::log;
36 
37  if (!(stan::length(y)
38  && stan::length(y_min)
39  && stan::length(alpha)))
40  return 0.0;
41 
42  T_partials_return logp(0.0);
43 
44  check_not_nan(function, "Random variable", y);
45  check_positive_finite(function, "Scale parameter", y_min);
46  check_positive_finite(function, "Shape parameter", alpha);
47  check_consistent_sizes(function,
48  "Random variable", y,
49  "Scale parameter", y_min,
50  "Shape parameter", alpha);
51 
53  return 0.0;
54 
56  scalar_seq_view<const T_scale> y_min_vec(y_min);
57  scalar_seq_view<const T_shape> alpha_vec(alpha);
58  size_t N = max_size(y, y_min, alpha);
59 
60  for (size_t n = 0; n < N; n++) {
61  if (y_vec[n] < y_min_vec[n])
62  return LOG_ZERO;
63  }
64 
66  operands_and_partials(y, y_min, alpha);
67 
69  T_partials_return, T_y> log_y(length(y));
71  for (size_t n = 0; n < length(y); n++)
72  log_y[n] = log(value_of(y_vec[n]));
73  }
74 
76  T_partials_return, T_y> inv_y(length(y));
78  for (size_t n = 0; n < length(y); n++)
79  inv_y[n] = 1 / value_of(y_vec[n]);
80  }
81 
83  T_partials_return, T_scale>
84  log_y_min(length(y_min));
86  for (size_t n = 0; n < length(y_min); n++)
87  log_y_min[n] = log(value_of(y_min_vec[n]));
88  }
89 
91  T_partials_return, T_shape> log_alpha(length(alpha));
93  for (size_t n = 0; n < length(alpha); n++)
94  log_alpha[n] = log(value_of(alpha_vec[n]));
95  }
96 
97  for (size_t n = 0; n < N; n++) {
98  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
100  logp += log_alpha[n];
102  logp += alpha_dbl * log_y_min[n];
104  logp -= alpha_dbl * log_y[n] + log_y[n];
105 
107  operands_and_partials.d_x1[n] -= alpha_dbl * inv_y[n] + inv_y[n];
109  operands_and_partials.d_x2[n] += alpha_dbl / value_of(y_min_vec[n]);
111  operands_and_partials.d_x3[n]
112  += 1 / alpha_dbl + log_y_min[n] - log_y[n];
113  }
114  return operands_and_partials.value(logp);
115  }
116 
117  template <typename T_y, typename T_scale, typename T_shape>
118  inline
120  pareto_lpdf(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
121  return pareto_lpdf<false>(y, y_min, alpha);
122  }
123 
124  }
125 }
126 #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
const double LOG_ZERO
Definition: constants.hpp:172
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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.
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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
VectorBuilder allocates type T1 values to be used as intermediate values.
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
return_type< T_y, T_scale, T_shape >::type pareto_lpdf(const T_y &y, const T_scale &y_min, const T_shape &alpha)
Definition: pareto_lpdf.hpp:30
VectorView< T_return_type, false, true > d_x1

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