1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LCCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LCCDF_HPP 17 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
19 const T_y& y,
const T_loc& mu,
const T_scale& lambda,
20 const T_shape& alpha) {
28 static const char*
function =
"pareto_type_2_lccdf";
32 T_partials_return P(0.0);
40 lambda,
"Shape parameter", alpha);
46 size_t N =
max_size(y, mu, lambda, alpha);
49 y, mu, lambda, alpha);
55 T_partials_return, T_y, T_loc, T_scale, T_shape>
56 a_over_lambda_plus_y(N);
60 log_1p_y_over_lambda(N);
62 for (
size_t i = 0; i < N; i++) {
63 const T_partials_return y_dbl =
value_of(y_vec[i]);
64 const T_partials_return mu_dbl =
value_of(mu_vec[i]);
65 const T_partials_return lambda_dbl =
value_of(lambda_vec[i]);
66 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
67 const T_partials_return temp = 1.0 + (y_dbl - mu_dbl) / lambda_dbl;
68 const T_partials_return log_temp =
log(temp);
70 ccdf_log[i] = -alpha_dbl * log_temp;
73 a_over_lambda_plus_y[i] = alpha_dbl / (y_dbl - mu_dbl + lambda_dbl);
76 log_1p_y_over_lambda[i] = log_temp;
79 for (
size_t n = 0; n < N; n++) {
80 const T_partials_return y_dbl =
value_of(y_vec[n]);
81 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
82 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
87 ops_partials.
edge1_.partials_[n] -= a_over_lambda_plus_y[n];
89 ops_partials.
edge2_.partials_[n] += a_over_lambda_plus_y[n];
91 ops_partials.
edge3_.partials_[n]
92 += a_over_lambda_plus_y[n] * (y_dbl - mu_dbl) / lambda_dbl;
94 ops_partials.
edge4_.partials_[n] -= log_1p_y_over_lambda[n];
96 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)
internal::ops_partials_edge< double, Op4 > edge4_
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.
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_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Check if y is greater or equal than low.
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
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lccdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
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_