1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LPDF_HPP 19 template <
bool propto,
typename T_y,
typename T_loc,
typename T_scale,
22 const T_y& y,
const T_loc& mu,
const T_scale& sigma,
const T_shape& alpha) {
23 static const char*
function =
"skew_normal_lpdf";
34 T_partials_return logp(0.0);
41 mu,
"Scale parameter", sigma,
"Shape paramter", alpha);
53 size_t N =
max_size(y, mu, sigma, alpha);
59 for (
size_t i = 0; i <
length(sigma); i++) {
60 inv_sigma[i] = 1.0 /
value_of(sigma_vec[i]);
65 for (
size_t n = 0; n < N; n++) {
66 const T_partials_return y_dbl =
value_of(y_vec[n]);
67 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
68 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
69 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
71 const T_partials_return y_minus_mu_over_sigma
72 = (y_dbl - mu_dbl) * inv_sigma[n];
73 const double pi_dbl =
pi();
76 logp -= 0.5 *
log(2.0 * pi_dbl);
78 logp -=
log(sigma_dbl);
80 logp -= y_minus_mu_over_sigma * y_minus_mu_over_sigma / 2.0;
84 T_partials_return deriv_logerf
86 *
exp(-alpha_dbl * y_minus_mu_over_sigma /
std::sqrt(2.0) * alpha_dbl
88 / (1 +
erf(alpha_dbl * y_minus_mu_over_sigma /
std::sqrt(2.0)));
90 ops_partials.
edge1_.partials_[n]
91 += -y_minus_mu_over_sigma / sigma_dbl
92 + deriv_logerf * alpha_dbl / (sigma_dbl *
std::sqrt(2.0));
94 ops_partials.
edge2_.partials_[n]
95 += y_minus_mu_over_sigma / sigma_dbl
96 + deriv_logerf * -alpha_dbl / (sigma_dbl *
std::sqrt(2.0));
98 ops_partials.
edge3_.partials_[n]
100 + y_minus_mu_over_sigma * y_minus_mu_over_sigma / sigma_dbl
101 - deriv_logerf * y_minus_mu_over_sigma * alpha_dbl
104 ops_partials.
edge4_.partials_[n]
105 += deriv_logerf * y_minus_mu_over_sigma /
std::sqrt(2.0);
107 return ops_partials.
build(logp);
110 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
113 const T_shape& alpha) {
114 return skew_normal_lpdf<false>(y, mu, sigma, alpha);
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.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
fvar< T > erf(const fvar< T > &x)
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_lpdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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.
VectorBuilder allocates type T1 values to be used as intermediate values.
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_