1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LPDF_HPP 15 #include <boost/random/normal_distribution.hpp> 16 #include <boost/random/variate_generator.hpp> 22 template <
bool propto,
23 typename T_y,
typename T_loc,
typename T_scale,
27 const T_inv_scale& lambda) {
28 static const char*
function(
"exp_mod_normal_lpdf");
42 T_partials_return logp(0.0);
50 "Location parameter", mu,
51 "Scale parameter", sigma,
52 "Inv_scale paramter", lambda);
63 operands_and_partials(y, mu, sigma, lambda);
69 size_t N =
max_size(y, mu, sigma, lambda);
71 for (
size_t n = 0; n < N; n++) {
72 const T_partials_return y_dbl =
value_of(y_vec[n]);
73 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
74 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
75 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
77 const T_partials_return pi_dbl = boost::math::constants::pi<double>();
82 logp +=
log(lambda_dbl);
85 * (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
86 +
log(
erfc((mu_dbl + lambda_dbl * sigma_dbl
88 / (
sqrt(2.0) * sigma_dbl)));
90 const T_partials_return deriv_logerfc
92 *
exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
94 * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
96 /
erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl
100 operands_and_partials.
d_x1[n]
102 + deriv_logerfc * -1.0 / (sigma_dbl *
std::sqrt(2.0));
104 operands_and_partials.
d_x2[n]
106 + deriv_logerfc / (sigma_dbl *
std::sqrt(2.0));
108 operands_and_partials.
d_x3[n]
109 += sigma_dbl * lambda_dbl * lambda_dbl
111 * (-mu_dbl / (sigma_dbl * sigma_dbl *
std::sqrt(2.0))
113 + y_dbl / (sigma_dbl * sigma_dbl *
std::sqrt(2.0)));
115 operands_and_partials.
d_x4[n]
116 += 1 / lambda_dbl + lambda_dbl * sigma_dbl * sigma_dbl
117 + mu_dbl - y_dbl + deriv_logerfc * sigma_dbl /
std::sqrt(2.0);
119 return operands_and_partials.
value(logp);
122 template <
typename T_y,
typename T_loc,
typename T_scale,
123 typename T_inv_scale>
127 const T_inv_scale& lambda) {
128 return exp_mod_normal_lpdf<false>(y, mu, sigma, lambda);
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.
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lpdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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)
fvar< T > erfc(const fvar< T > &x)
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