1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
4 #include <boost/random/variate_generator.hpp>
5 #include <boost/math/distributions.hpp>
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
27 const T_shape& alpha) {
28 static const char*
function(
"stan::math::skew_normal_cdf");
40 T_partials_return cdf(1.0);
57 "Location parameter", mu,
58 "Scale parameter", sigma,
59 "Shape paramter", alpha);
62 operands_and_partials(y, mu, sigma, alpha);
72 size_t N =
max_size(y, mu, sigma, alpha);
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
92 const T_partials_return deriv_erfc = SQRT_TWO_OVER_PI * 0.5
93 *
exp(-scaled_diff_sq)
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)
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_;
114 operands_and_partials.
d_x1[n] *= cdf;
118 operands_and_partials.
d_x2[n] *= cdf;
122 operands_and_partials.
d_x3[n] *= cdf;
126 operands_and_partials.
d_x4[n] *= cdf;
129 return operands_and_partials.
to_var(cdf, y, mu, sigma, alpha);
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.
size_t length(const std::vector< T > &x)
fvar< T > erf(const fvar< T > &x)
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)
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, .
fvar< T > exp(const fvar< T > &x)
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)
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)
double pi()
Return the value of pi.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...