1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
17 #include <boost/random/variate_generator.hpp>
18 #include <boost/math/distributions.hpp>
25 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
26 typename return_type<T_y, T_loc, T_scale, T_shape>::type
28 const T_shape& alpha) {
29 static const char*
function(
"stan::math::skew_normal_cdf");
41 T_partials_return cdf(1.0);
58 "Location parameter", mu,
59 "Scale parameter", sigma,
60 "Shape paramter", alpha);
63 operands_and_partials(y, mu, sigma, alpha);
73 size_t N =
max_size(y, mu, sigma, alpha);
76 for (
size_t n = 0; n < N; n++) {
77 const T_partials_return y_dbl =
value_of(y_vec[n]);
78 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
79 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
80 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
81 const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
82 const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
83 const T_partials_return diff_sq = diff * diff;
84 const T_partials_return scaled_diff = diff /
SQRT_2;
85 const T_partials_return scaled_diff_sq = diff_sq * 0.5;
86 const T_partials_return cdf_ = 0.5 *
erfc(-scaled_diff) - 2
93 const T_partials_return deriv_erfc = SQRT_TWO_OVER_PI * 0.5
94 *
exp(-scaled_diff_sq)
96 const T_partials_return deriv_owens =
erf(alpha_dbl * scaled_diff)
97 *
exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI / (-2.0 *
pi()) / sigma_dbl;
98 const T_partials_return rep_deriv = (-2.0 * deriv_owens + deriv_erfc)
102 operands_and_partials.
d_x1[n] += rep_deriv;
104 operands_and_partials.
d_x2[n] -= rep_deriv;
106 operands_and_partials.
d_x3[n] -= rep_deriv * diff;
108 operands_and_partials.
d_x4[n] += -2.0 *
exp(-0.5 * diff_sq
109 * (1.0 + alpha_dbl_sq))
110 / ((1 + alpha_dbl_sq) * 2.0 *
pi()) / cdf_;
115 operands_and_partials.
d_x1[n] *= cdf;
119 operands_and_partials.
d_x2[n] *= cdf;
123 operands_and_partials.
d_x3[n] *= cdf;
127 operands_and_partials.
d_x4[n] *= cdf;
130 return operands_and_partials.
value(cdf);
VectorView< T_return_type, false, true > d_x2
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)
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.
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
fvar< T > erf(const fvar< T > &x)
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
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, .
fvar< T > exp(const fvar< T > &x)
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
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)
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.
fvar< T > erfc(const fvar< T > &x)
double pi()
Return the value of pi.
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4