1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LCCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LCCDF_HPP 18 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
20 const T_y& y,
const T_loc& mu,
const T_scale& sigma,
const T_shape& alpha) {
21 static const char*
function =
"skew_normal_lccdf";
26 T_partials_return ccdf_log(0.0);
38 mu,
"Scale parameter", sigma,
"Shape paramter", alpha);
50 size_t N =
max_size(y, mu, sigma, alpha);
51 const double SQRT_TWO_OVER_PI =
std::sqrt(2.0 /
pi());
53 for (
size_t n = 0; n < N; n++) {
54 const T_partials_return y_dbl =
value_of(y_vec[n]);
55 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
56 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
57 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
58 const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
59 const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
60 const T_partials_return diff_sq = diff * diff;
61 const T_partials_return scaled_diff = diff /
SQRT_2;
62 const T_partials_return scaled_diff_sq = diff_sq * 0.5;
63 const T_partials_return ccdf_log_
64 = 1.0 - 0.5 *
erfc(-scaled_diff) + 2 *
owens_t(diff, alpha_dbl);
66 ccdf_log +=
log(ccdf_log_);
68 const T_partials_return deriv_erfc
69 = SQRT_TWO_OVER_PI * 0.5 *
exp(-scaled_diff_sq) / sigma_dbl;
70 const T_partials_return deriv_owens
71 =
erf(alpha_dbl * scaled_diff) *
exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI
72 / (-2.0 *
pi()) / sigma_dbl;
73 const T_partials_return rep_deriv
74 = (-2.0 * deriv_owens + deriv_erfc) / ccdf_log_;
77 ops_partials.
edge1_.partials_[n] -= rep_deriv;
79 ops_partials.
edge2_.partials_[n] += rep_deriv;
81 ops_partials.
edge3_.partials_[n] += rep_deriv * diff;
83 ops_partials.
edge4_.partials_[n]
84 -= -2.0 *
exp(-0.5 * diff_sq * (1.0 + alpha_dbl_sq))
85 / ((1 + alpha_dbl_sq) * 2.0 *
pi()) / ccdf_log_;
87 return ops_partials.
build(ccdf_log);
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
fvar< T > sqrt(const fvar< T > &x)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
fvar< T > log(const fvar< T > &x)
internal::ops_partials_edge< double, Op4 > edge4_
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
fvar< T > erf(const fvar< T > &x)
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Return Owen's T function applied to the specified arguments.
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_lccdf(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, .
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
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.
size_t max_size(const T1 &x1, const T2 &x2)
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
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.
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_