1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LPDF_HPP 19 #include <boost/random/variate_generator.hpp> 20 #include <boost/math/distributions.hpp> 26 template <
bool propto,
27 typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
30 const T_shape& alpha) {
31 static const char*
function(
"skew_normal_lpdf");
33 T_scale, T_shape>::type
46 T_partials_return logp(0.0);
54 "Location parameter", mu,
55 "Scale parameter", sigma,
56 "Shape paramter", alpha);
62 operands_and_partials(y, mu, sigma, alpha);
70 size_t N =
max_size(y, mu, sigma, alpha);
74 T_partials_return, T_scale> log_sigma(
length(sigma));
75 for (
size_t i = 0; i <
length(sigma); i++) {
76 inv_sigma[i] = 1.0 /
value_of(sigma_vec[i]);
81 for (
size_t n = 0; n < N; n++) {
82 const T_partials_return y_dbl =
value_of(y_vec[n]);
83 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
84 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
85 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
87 const T_partials_return y_minus_mu_over_sigma
88 = (y_dbl - mu_dbl) * inv_sigma[n];
89 const double pi_dbl =
pi();
92 logp -= 0.5 *
log(2.0 * pi_dbl);
94 logp -=
log(sigma_dbl);
96 logp -= y_minus_mu_over_sigma * y_minus_mu_over_sigma / 2.0;
98 logp +=
log(
erfc(-alpha_dbl * y_minus_mu_over_sigma
101 T_partials_return deriv_logerf
103 *
exp(-alpha_dbl * y_minus_mu_over_sigma /
std::sqrt(2.0)
104 * alpha_dbl * y_minus_mu_over_sigma /
std::sqrt(2.0))
105 / (1 +
erf(alpha_dbl * y_minus_mu_over_sigma
108 operands_and_partials.
d_x1[n]
109 += -y_minus_mu_over_sigma / sigma_dbl
110 + deriv_logerf * alpha_dbl / (sigma_dbl *
std::sqrt(2.0));
112 operands_and_partials.
d_x2[n]
113 += y_minus_mu_over_sigma / sigma_dbl
114 + deriv_logerf * -alpha_dbl / (sigma_dbl *
std::sqrt(2.0));
116 operands_and_partials.
d_x3[n]
118 + y_minus_mu_over_sigma * y_minus_mu_over_sigma / sigma_dbl
119 - deriv_logerf * y_minus_mu_over_sigma * alpha_dbl
122 operands_and_partials.
d_x4[n]
123 += deriv_logerf * y_minus_mu_over_sigma /
std::sqrt(2.0);
125 return operands_and_partials.
value(logp);
128 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
132 const T_shape& alpha) {
133 return skew_normal_lpdf<false>(y, mu, sigma, alpha);
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)
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)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
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)
VectorBuilder allocates type T1 values to be used as intermediate values.
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