1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LOG_HPP
4 #include <boost/random/variate_generator.hpp>
5 #include <boost/math/distributions.hpp>
24 template <
bool propto,
25 typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
26 typename return_type<T_y, T_loc, T_scale, T_shape>::type
28 const T_shape& alpha) {
29 static const char*
function(
"stan::math::skew_normal_log");
31 T_scale, T_shape>::type
52 T_partials_return logp(0.0);
61 "Location parameter", mu,
62 "Scale parameter", sigma,
63 "Shape paramter", alpha);
71 operands_and_partials(y, mu, sigma, alpha);
81 size_t N =
max_size(y, mu, sigma, alpha);
85 T_partials_return, T_scale> log_sigma(
length(sigma));
86 for (
size_t i = 0; i <
length(sigma); i++) {
87 inv_sigma[i] = 1.0 /
value_of(sigma_vec[i]);
92 for (
size_t n = 0; n < N; n++) {
94 const T_partials_return y_dbl =
value_of(y_vec[n]);
95 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
96 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
97 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
100 const T_partials_return y_minus_mu_over_sigma
101 = (y_dbl - mu_dbl) * inv_sigma[n];
106 logp -= 0.5 *
log(2.0 * pi_dbl);
108 logp -=
log(sigma_dbl);
110 logp -= y_minus_mu_over_sigma * y_minus_mu_over_sigma / 2.0;
112 logp +=
log(
erfc(-alpha_dbl * y_minus_mu_over_sigma
116 T_partials_return deriv_logerf
118 *
exp(-alpha_dbl * y_minus_mu_over_sigma /
std::sqrt(2.0)
119 * alpha_dbl * y_minus_mu_over_sigma /
std::sqrt(2.0))
120 / (1 +
erf(alpha_dbl * y_minus_mu_over_sigma
123 operands_and_partials.
d_x1[n]
124 += -y_minus_mu_over_sigma / sigma_dbl
125 + deriv_logerf * alpha_dbl / (sigma_dbl *
std::sqrt(2.0));
127 operands_and_partials.
d_x2[n]
128 += y_minus_mu_over_sigma / sigma_dbl
129 + deriv_logerf * -alpha_dbl / (sigma_dbl *
std::sqrt(2.0));
131 operands_and_partials.
d_x3[n]
133 + y_minus_mu_over_sigma * y_minus_mu_over_sigma / sigma_dbl
134 - deriv_logerf * y_minus_mu_over_sigma * alpha_dbl
137 operands_and_partials.
d_x4[n]
138 += deriv_logerf * y_minus_mu_over_sigma /
std::sqrt(2.0);
140 return operands_and_partials.
to_var(logp, y, mu, sigma, alpha);
143 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
147 const T_shape& alpha) {
148 return skew_normal_log<false>(y, mu, sigma, alpha);
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_log(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.
fvar< T > log(const fvar< T > &x)
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)
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
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...
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...