1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_LCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_LCDF_HPP 18 template <
typename T_y,
typename T_scale,
typename T_shape>
20 const T_y& y,
const T_scale& y_min,
const T_shape& alpha) {
27 static const char*
function =
"pareto_lcdf";
32 T_partials_return P(0.0);
39 y_min,
"Shape parameter", alpha);
44 size_t N =
max_size(y, y_min, alpha);
55 for (
size_t n = 0; n < N; n++) {
58 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
59 return ops_partials.
build(0.0);
62 const T_partials_return log_dbl
64 const T_partials_return y_min_inv_dbl = 1.0 /
value_of(y_min_vec[n]);
65 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
67 const T_partials_return Pn = 1.0 -
exp(alpha_dbl * log_dbl);
72 ops_partials.
edge1_.partials_[n]
73 += alpha_dbl * y_min_inv_dbl *
exp((alpha_dbl + 1) * log_dbl) / Pn;
75 ops_partials.
edge2_.partials_[n]
76 -= alpha_dbl * y_min_inv_dbl *
exp(alpha_dbl * log_dbl) / Pn;
78 ops_partials.
edge3_.partials_[n]
79 -=
exp(alpha_dbl * log_dbl) * log_dbl / Pn;
81 return ops_partials.
build(P);
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
fvar< T > log(const fvar< T > &x)
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
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.
return_type< T_y, T_scale, T_shape >::type pareto_lcdf(const T_y &y, const T_scale &y_min, const T_shape &alpha)
size_t max_size(const T1 &x1, const T2 &x2)
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_
double negative_infinity()
Return negative infinity.