Stan Math Library  2.20.0
reverse mode automatic differentiation
pareto_type_2_lpdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LPDF_HPP
3 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
18 // pareto_type_2(y|lambda, alpha) [y >= 0; lambda > 0; alpha > 0]
19 template <bool propto, typename T_y, typename T_loc, typename T_scale,
20  typename T_shape>
22  const T_y& y, const T_loc& mu, const T_scale& lambda,
23  const T_shape& alpha) {
24  static const char* function = "pareto_type_2_lpdf";
25  typedef
27  T_partials_return;
28 
29  using std::log;
30 
31  if (size_zero(y, mu, lambda, alpha))
32  return 0.0;
33 
34  T_partials_return logp(0.0);
35 
36  check_greater_or_equal(function, "Random variable", y, mu);
37  check_not_nan(function, "Random variable", y);
38  check_positive_finite(function, "Scale parameter", lambda);
39  check_positive_finite(function, "Shape parameter", alpha);
40  check_consistent_sizes(function, "Random variable", y, "Scale parameter",
41  lambda, "Shape parameter", alpha);
42 
44  return 0.0;
45 
46  scalar_seq_view<T_y> y_vec(y);
47  scalar_seq_view<T_loc> mu_vec(mu);
48  scalar_seq_view<T_scale> lambda_vec(lambda);
49  scalar_seq_view<T_shape> alpha_vec(alpha);
50  size_t N = max_size(y, mu, lambda, alpha);
51 
53  y, mu, lambda, alpha);
54 
56  T_partials_return, T_y, T_loc, T_scale>
57  log1p_scaled_diff(N);
59  for (size_t n = 0; n < N; n++)
60  log1p_scaled_diff[n] = log1p((value_of(y_vec[n]) - value_of(mu_vec[n]))
61  / value_of(lambda_vec[n]));
62  }
63 
65  T_scale>
66  log_lambda(length(lambda));
68  for (size_t n = 0; n < length(lambda); n++)
69  log_lambda[n] = log(value_of(lambda_vec[n]));
70  }
71 
73  T_shape>
74  log_alpha(length(alpha));
76  for (size_t n = 0; n < length(alpha); n++)
77  log_alpha[n] = log(value_of(alpha_vec[n]));
78  }
79 
80  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
81  inv_alpha(length(alpha));
83  for (size_t n = 0; n < length(alpha); n++)
84  inv_alpha[n] = 1 / value_of(alpha_vec[n]);
85  }
86 
87  for (size_t n = 0; n < N; n++) {
88  const T_partials_return y_dbl = value_of(y_vec[n]);
89  const T_partials_return mu_dbl = value_of(mu_vec[n]);
90  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
91  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
92  const T_partials_return sum_dbl = lambda_dbl + y_dbl - mu_dbl;
93  const T_partials_return inv_sum = 1.0 / sum_dbl;
94  const T_partials_return alpha_div_sum = alpha_dbl / sum_dbl;
95  const T_partials_return deriv_1_2 = inv_sum + alpha_div_sum;
96 
98  logp += log_alpha[n];
100  logp -= log_lambda[n];
102  logp -= (alpha_dbl + 1.0) * log1p_scaled_diff[n];
103 
105  ops_partials.edge1_.partials_[n] -= deriv_1_2;
107  ops_partials.edge2_.partials_[n] += deriv_1_2;
109  ops_partials.edge3_.partials_[n]
110  -= alpha_div_sum * (mu_dbl - y_dbl) / lambda_dbl + inv_sum;
112  ops_partials.edge4_.partials_[n] += inv_alpha[n] - log1p_scaled_diff[n];
113  }
114  return ops_partials.build(logp);
115 }
116 
117 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
119 pareto_type_2_lpdf(const T_y& y, const T_loc& mu, const T_scale& lambda,
120  const T_shape& alpha) {
121  return pareto_type_2_lpdf<false>(y, mu, lambda, alpha);
122 }
123 
124 } // namespace math
125 } // namespace stan
126 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
internal::ops_partials_edge< double, Op4 > edge4_
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
void check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Check if y is greater or equal than low.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lpdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:12
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

     [ Stan Home Page ] © 2011–2018, Stan Development Team.