1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_LOG_HPP
4 #include <boost/random/exponential_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
21 template <
typename T_y,
typename T_scale,
typename T_shape>
22 typename return_type<T_y, T_scale, T_shape>::type
32 static const char*
function(
"stan::math::pareto_cdf_log");
43 T_partials_return P(0.0);
51 "Scale parameter", y_min,
52 "Shape parameter", alpha);
58 size_t N =
max_size(y, y_min, alpha);
61 operands_and_partials(y, y_min, alpha);
74 for (
size_t n = 0; n < N; n++) {
77 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
78 return operands_and_partials.
to_var(0.0, y, y_min, alpha);
82 const T_partials_return log_dbl =
log(
value_of(y_min_vec[n])
84 const T_partials_return y_min_inv_dbl = 1.0 /
value_of(y_min_vec[n]);
85 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
88 const T_partials_return Pn = 1.0 -
exp(alpha_dbl * log_dbl);
93 operands_and_partials.
d_x1[n]
94 += alpha_dbl * y_min_inv_dbl *
exp((alpha_dbl + 1) * log_dbl) / Pn;
96 operands_and_partials.
d_x2[n]
97 -= alpha_dbl * y_min_inv_dbl *
exp(alpha_dbl * log_dbl) / Pn;
99 operands_and_partials.
d_x3[n]
100 -=
exp(alpha_dbl * log_dbl) * log_dbl / Pn;
103 return operands_and_partials.
to_var(P, y, y_min, alpha);
bool check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Return true if y is greater or equal than low.
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)
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)
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
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
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
return_type< T_y, T_scale, T_shape >::type pareto_cdf_log(const T_y &y, const T_scale &y_min, const T_shape &alpha)
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
double negative_infinity()
Return negative infinity.