Stan Math Library  2.15.0
reverse mode automatic differentiation
pareto_type_2_lcdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LCDF_HPP
3 
18 #include <boost/random/variate_generator.hpp>
19 #include <cmath>
20 
21 namespace stan {
22  namespace math {
23 
24  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
26  pareto_type_2_lcdf(const T_y& y, const T_loc& mu,
27  const T_scale& lambda, const T_shape& alpha) {
28  typedef
30  T_partials_return;
31 
32  if ( !( stan::length(y)
33  && stan::length(mu)
34  && stan::length(lambda)
35  && stan::length(alpha) ) )
36  return 0.0;
37 
38  static const char* function("pareto_type_2_lcdf");
39 
40  using std::log;
41 
42  T_partials_return P(0.0);
43 
44  check_greater_or_equal(function, "Random variable", y, mu);
45  check_not_nan(function, "Random variable", y);
46  check_nonnegative(function, "Random variable", y);
47  check_positive_finite(function, "Scale parameter", lambda);
48  check_positive_finite(function, "Shape parameter", alpha);
49  check_consistent_sizes(function,
50  "Random variable", y,
51  "Scale parameter", lambda,
52  "Shape parameter", alpha);
53 
56  scalar_seq_view<const T_scale> lambda_vec(lambda);
57  scalar_seq_view<const T_shape> alpha_vec(alpha);
58  size_t N = max_size(y, mu, lambda, alpha);
59 
61  operands_and_partials(y, mu, lambda, alpha);
62 
63  VectorBuilder<true, T_partials_return,
64  T_y, T_loc, T_scale, T_shape>
65  cdf_log(N);
66 
67  VectorBuilder<true, T_partials_return,
68  T_y, T_loc, T_scale, T_shape>
69  inv_p1_pow_alpha_minus_one(N);
70 
72  T_partials_return, T_y, T_loc, T_scale, T_shape>
73  log_1p_y_over_lambda(N);
74 
75  for (size_t i = 0; i < N; i++) {
76  const T_partials_return temp = 1.0 + (value_of(y_vec[i])
77  - value_of(mu_vec[i]))
78  / value_of(lambda_vec[i]);
79  const T_partials_return p1_pow_alpha
80  = pow(temp, value_of(alpha_vec[i]));
81  cdf_log[i] = log1m(1.0 / p1_pow_alpha);
82 
83  inv_p1_pow_alpha_minus_one[i] = 1.0 / (p1_pow_alpha - 1.0);
84 
86  log_1p_y_over_lambda[i] = log(temp);
87  }
88 
89  for (size_t n = 0; n < N; n++) {
90  const T_partials_return y_dbl = value_of(y_vec[n]);
91  const T_partials_return mu_dbl = value_of(mu_vec[n]);
92  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
93  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
94 
95  const T_partials_return grad_1_2 = alpha_dbl
96  * inv_p1_pow_alpha_minus_one[n] / (lambda_dbl - mu_dbl + y_dbl);
97 
98  P += cdf_log[n];
99 
101  operands_and_partials.d_x1[n] += grad_1_2;
103  operands_and_partials.d_x2[n] -= grad_1_2;
105  operands_and_partials.d_x3[n] += (mu_dbl - y_dbl) * grad_1_2
106  / lambda_dbl;
108  operands_and_partials.d_x4[n] += log_1p_y_over_lambda[n]
109  * inv_p1_pow_alpha_minus_one[n];
110  }
111  return operands_and_partials.value(P);
112  }
113 
114  }
115 }
116 #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
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lcdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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.
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.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:13
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4

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