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pareto_type_2_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_HPP
3 
4 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 namespace stan {
21  namespace math {
22 
23  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
24  typename return_type<T_y, T_loc, T_scale, T_shape>::type
25  pareto_type_2_cdf(const T_y& y, const T_loc& mu,
26  const T_scale& lambda, const T_shape& alpha) {
27  typedef
29  T_partials_return;
30 
31  // Check sizes
32  // Size checks
33  if ( !( stan::length(y)
34  && stan::length(mu)
35  && stan::length(lambda)
36  && stan::length(alpha) ) )
37  return 1.0;
38 
39  // Check errors
40  static const char* function("stan::math::pareto_type_2_cdf");
41 
50  using std::log;
51 
52  T_partials_return P(1.0);
53 
54  check_greater_or_equal(function, "Random variable", y, mu);
55  check_not_nan(function, "Random variable", y);
56  check_nonnegative(function, "Random variable", y);
57  check_positive_finite(function, "Scale parameter", lambda);
58  check_positive_finite(function, "Shape parameter", alpha);
59  check_consistent_sizes(function,
60  "Random variable", y,
61  "Scale parameter", lambda,
62  "Shape parameter", alpha);
63 
64  // Wrap arguments in vectors
65  VectorView<const T_y> y_vec(y);
66  VectorView<const T_loc> mu_vec(mu);
67  VectorView<const T_scale> lambda_vec(lambda);
68  VectorView<const T_shape> alpha_vec(alpha);
69  size_t N = max_size(y, mu, lambda, alpha);
70 
72  operands_and_partials(y, mu, lambda, alpha);
73 
74  VectorBuilder<true, T_partials_return,
75  T_y, T_loc, T_scale, T_shape>
76  p1_pow_alpha(N);
77 
79  T_partials_return, T_y, T_loc, T_scale, T_shape>
80  grad_1_2(N);
81 
83  T_partials_return, T_y, T_loc, T_scale, T_shape>
84  grad_3(N);
85 
86  for (size_t i = 0; i < N; i++) {
87  const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
88  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
89  const T_partials_return temp = 1 + (value_of(y_vec[i])
90  - value_of(mu_vec[i]))
91  / lambda_dbl;
92  p1_pow_alpha[i] = pow(temp, -alpha_dbl);
93 
95  grad_1_2[i] = p1_pow_alpha[i] / temp * alpha_dbl / lambda_dbl;
96 
98  grad_3[i] = log(temp) * p1_pow_alpha[i];
99  }
100 
101  // Compute vectorized CDF and its gradients
102 
103  for (size_t n = 0; n < N; n++) {
104  // Pull out values
105  const T_partials_return y_dbl = value_of(y_vec[n]);
106  const T_partials_return mu_dbl = value_of(mu_vec[n]);
107  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
108 
109  const T_partials_return Pn = 1.0 - p1_pow_alpha[n];
110 
111  // Compute
112  P *= Pn;
113 
115  operands_and_partials.d_x1[n] += grad_1_2[n] / Pn;
117  operands_and_partials.d_x2[n] -= grad_1_2[n] / Pn;
119  operands_and_partials.d_x3[n] += (mu_dbl - y_dbl)
120  * grad_1_2[n] / lambda_dbl / Pn;
122  operands_and_partials.d_x4[n] += grad_3[n] / Pn;
123  }
124 
126  for (size_t n = 0; n < stan::length(y); ++n)
127  operands_and_partials.d_x1[n] *= P;
128  }
130  for (size_t n = 0; n < stan::length(mu); ++n)
131  operands_and_partials.d_x2[n] *= P;
132  }
134  for (size_t n = 0; n < stan::length(lambda); ++n)
135  operands_and_partials.d_x3[n] *= P;
136  }
138  for (size_t n = 0; n < stan::length(alpha); ++n)
139  operands_and_partials.d_x4[n] *= P;
140  }
141 
142  return operands_and_partials.to_var(P, y, mu, lambda, alpha);
143  }
144  }
145 }
146 #endif
bool check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Return true if y is greater or equal than low.
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
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:15
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_cdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.

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