1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CCDF_LOG_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CCDF_LOG_HPP 17 #include <boost/random/variate_generator.hpp> 18 #include <boost/math/distributions.hpp> 24 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
27 const T_shape& alpha) {
28 static const char*
function(
"skew_normal_ccdf_log");
33 T_partials_return ccdf_log(0.0);
49 "Location parameter", mu,
50 "Scale parameter", sigma,
51 "Shape paramter", alpha);
54 operands_and_partials(y, mu, sigma, alpha);
63 size_t N =
max_size(y, mu, sigma, alpha);
64 const double SQRT_TWO_OVER_PI =
std::sqrt(2.0 /
pi());
66 for (
size_t n = 0; n < N; n++) {
67 const T_partials_return y_dbl =
value_of(y_vec[n]);
68 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
69 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
70 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
71 const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
72 const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
73 const T_partials_return diff_sq = diff * diff;
74 const T_partials_return scaled_diff = diff /
SQRT_2;
75 const T_partials_return scaled_diff_sq = diff_sq * 0.5;
76 const T_partials_return ccdf_log_ = 1.0 - 0.5 *
erfc(-scaled_diff)
79 ccdf_log +=
log(ccdf_log_);
81 const T_partials_return deriv_erfc = SQRT_TWO_OVER_PI * 0.5
82 *
exp(-scaled_diff_sq) / sigma_dbl;
83 const T_partials_return deriv_owens =
erf(alpha_dbl * scaled_diff)
84 *
exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI / (-2.0 *
pi()) / sigma_dbl;
85 const T_partials_return rep_deriv = (-2.0 * deriv_owens + deriv_erfc)
89 operands_and_partials.
d_x1[n] -= rep_deriv;
91 operands_and_partials.
d_x2[n] += rep_deriv;
93 operands_and_partials.
d_x3[n] += rep_deriv * diff;
95 operands_and_partials.
d_x4[n] -= -2.0 *
exp(-0.5 * diff_sq
96 * (1.0 + alpha_dbl_sq))
97 / ((1 + alpha_dbl_sq) * 2.0 *
pi()) / ccdf_log_;
99 return operands_and_partials.
value(ccdf_log);
VectorView< T_return_type, false, true > d_x2
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
fvar< T > sqrt(const fvar< T > &x)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > log(const fvar< T > &x)
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)
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
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Return Owen's T function applied to the specified arguments.
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_ccdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
const double SQRT_2
The value of the square root of 2, .
fvar< T > exp(const fvar< T > &x)
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)
fvar< T > erfc(const fvar< T > &x)
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
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[].
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.
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4