1 #ifndef STAN_MATH_PRIM_SCAL_PROB_FRECHET_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_FRECHET_LPDF_HPP 4 #include <boost/random/weibull_distribution.hpp> 5 #include <boost/random/variate_generator.hpp> 30 template <
bool propto,
31 typename T_y,
typename T_shape,
typename T_scale>
33 frechet_lpdf(
const T_y& y,
const T_shape& alpha,
const T_scale& sigma) {
34 static const char*
function(
"frechet_lpdf");
45 T_partials_return logp(0.0);
51 "Shape parameter", alpha,
52 "Scale parameter", sigma);
60 size_t N =
max_size(y, alpha, sigma);
63 T_partials_return, T_shape> log_alpha(
length(alpha));
64 for (
size_t i = 0; i <
length(alpha); i++)
69 T_partials_return, T_y> log_y(
length(y));
70 for (
size_t i = 0; i <
length(y); i++)
75 T_partials_return, T_scale> log_sigma(
length(sigma));
76 for (
size_t i = 0; i <
length(sigma); i++)
81 T_partials_return, T_y> inv_y(
length(y));
82 for (
size_t i = 0; i <
length(y); i++)
87 T_partials_return, T_y, T_shape, T_scale>
88 sigma_div_y_pow_alpha(N);
89 for (
size_t i = 0; i < N; i++)
91 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
92 sigma_div_y_pow_alpha[i] =
pow(inv_y[i] *
value_of(sigma_vec[i]),
97 operands_and_partials(y, alpha, sigma);
98 for (
size_t n = 0; n < N; n++) {
99 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
101 logp += log_alpha[n];
103 logp -= (alpha_dbl+1.0)*log_y[n];
105 logp += alpha_dbl*log_sigma[n];
107 logp -= sigma_div_y_pow_alpha[n];
110 const T_partials_return inv_y_dbl =
value_of(inv_y[n]);
111 operands_and_partials.
d_x1[n]
112 += -(alpha_dbl+1.0) * inv_y_dbl
113 + alpha_dbl * sigma_div_y_pow_alpha[n] * inv_y_dbl;
116 operands_and_partials.
d_x2[n]
118 + (1.0 - sigma_div_y_pow_alpha[n]) * (log_sigma[n] - log_y[n]);
120 operands_and_partials.
d_x3[n]
121 += alpha_dbl /
value_of(sigma_vec[n])
122 * (1 - sigma_div_y_pow_alpha[n]);
124 return operands_and_partials.
value(logp);
127 template <
typename T_y,
typename T_shape,
typename T_scale>
130 frechet_lpdf(
const T_y& y,
const T_shape& alpha,
const T_scale& sigma) {
131 return frechet_lpdf<false>(y, alpha, sigma);
return_type< T_y, T_shape, T_scale >::type frechet_lpdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
VectorView< T_return_type, false, true > d_x2
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)
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.
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.
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
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.
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
VectorView< T_return_type, false, true > d_x1