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skew_normal_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
3 
4 #include <boost/random/variate_generator.hpp>
5 #include <boost/math/distributions.hpp>
18 #include <cmath>
19 
20 namespace stan {
21 
22  namespace math {
23 
24  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
25  typename return_type<T_y, T_loc, T_scale, T_shape>::type
26  skew_normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
27  const T_shape& alpha) {
28  static const char* function("stan::math::skew_normal_cdf");
29  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
30  T_shape>::type
31  T_partials_return;
32 
37  using stan::math::owens_t;
39 
40  T_partials_return cdf(1.0);
41 
42  // check if any vectors are zero length
43  if (!(stan::length(y)
44  && stan::length(mu)
45  && stan::length(sigma)
46  && stan::length(alpha)))
47  return cdf;
48 
49  check_not_nan(function, "Random variable", y);
50  check_finite(function, "Location parameter", mu);
51  check_not_nan(function, "Scale parameter", sigma);
52  check_positive(function, "Scale parameter", sigma);
53  check_finite(function, "Shape parameter", alpha);
54  check_not_nan(function, "Shape parameter", alpha);
55  check_consistent_sizes(function,
56  "Random variable", y,
57  "Location parameter", mu,
58  "Scale parameter", sigma,
59  "Shape paramter", alpha);
60 
62  operands_and_partials(y, mu, sigma, alpha);
63 
64  using stan::math::SQRT_2;
65  using stan::math::pi;
66  using std::exp;
67 
68  VectorView<const T_y> y_vec(y);
69  VectorView<const T_loc> mu_vec(mu);
70  VectorView<const T_scale> sigma_vec(sigma);
71  VectorView<const T_shape> alpha_vec(alpha);
72  size_t N = max_size(y, mu, sigma, alpha);
73  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / stan::math::pi());
74 
75  for (size_t n = 0; n < N; n++) {
76  const T_partials_return y_dbl = value_of(y_vec[n]);
77  const T_partials_return mu_dbl = value_of(mu_vec[n]);
78  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
79  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
80  const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
81  const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
82  const T_partials_return diff_sq = diff * diff;
83  const T_partials_return scaled_diff = diff / SQRT_2;
84  const T_partials_return scaled_diff_sq = diff_sq * 0.5;
85  const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff) - 2
86  * owens_t(diff, alpha_dbl);
87 
88  // cdf
89  cdf *= cdf_;
90 
91  // gradients
92  const T_partials_return deriv_erfc = SQRT_TWO_OVER_PI * 0.5
93  * exp(-scaled_diff_sq)
94  / sigma_dbl;
95  const T_partials_return deriv_owens = erf(alpha_dbl * scaled_diff)
96  * exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI / (-2.0 * pi()) / sigma_dbl;
97  const T_partials_return rep_deriv = (-2.0 * deriv_owens + deriv_erfc)
98  / cdf_;
99 
101  operands_and_partials.d_x1[n] += rep_deriv;
103  operands_and_partials.d_x2[n] -= rep_deriv;
105  operands_and_partials.d_x3[n] -= rep_deriv * diff;
107  operands_and_partials.d_x4[n] += -2.0 * exp(-0.5 * diff_sq
108  * (1.0 + alpha_dbl_sq))
109  / ((1 + alpha_dbl_sq) * 2.0 * pi()) / cdf_;
110  }
111 
113  for (size_t n = 0; n < stan::length(y); ++n)
114  operands_and_partials.d_x1[n] *= cdf;
115  }
117  for (size_t n = 0; n < stan::length(mu); ++n)
118  operands_and_partials.d_x2[n] *= cdf;
119  }
121  for (size_t n = 0; n < stan::length(sigma); ++n)
122  operands_and_partials.d_x3[n] *= cdf;
123  }
125  for (size_t n = 0; n < stan::length(alpha); ++n)
126  operands_and_partials.d_x4[n] *= cdf;
127  }
128 
129  return operands_and_partials.to_var(cdf, y, mu, sigma, alpha);
130  }
131  }
132 }
133 #endif
134 
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:15
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
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)
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Definition: owens_t.hpp:14
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...
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:21
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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...
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
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 > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
double pi()
Return the value of pi.
Definition: constants.hpp:86
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41

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