1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LPDF_HPP 19 template <
bool propto,
typename T_y,
typename T_loc,
typename T_scale,
22 const T_y& y,
const T_loc& mu,
const T_scale& lambda,
23 const T_shape& alpha) {
24 static const char*
function =
"pareto_type_2_lpdf";
34 T_partials_return logp(0.0);
41 lambda,
"Shape parameter", alpha);
50 size_t N =
max_size(y, mu, lambda, alpha);
53 y, mu, lambda, alpha);
56 T_partials_return, T_y, T_loc, T_scale>
59 for (
size_t n = 0; n < N; n++)
66 log_lambda(
length(lambda));
68 for (
size_t n = 0; n <
length(lambda); n++)
76 for (
size_t n = 0; n <
length(alpha); n++)
83 for (
size_t n = 0; n <
length(alpha); n++)
84 inv_alpha[n] = 1 /
value_of(alpha_vec[n]);
87 for (
size_t n = 0; n < N; n++) {
88 const T_partials_return y_dbl =
value_of(y_vec[n]);
89 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
90 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
91 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
92 const T_partials_return sum_dbl = lambda_dbl + y_dbl - mu_dbl;
93 const T_partials_return inv_sum = 1.0 / sum_dbl;
94 const T_partials_return alpha_div_sum = alpha_dbl / sum_dbl;
95 const T_partials_return deriv_1_2 = inv_sum + alpha_div_sum;
100 logp -= log_lambda[n];
102 logp -= (alpha_dbl + 1.0) * log1p_scaled_diff[n];
105 ops_partials.
edge1_.partials_[n] -= deriv_1_2;
107 ops_partials.
edge2_.partials_[n] += deriv_1_2;
109 ops_partials.
edge3_.partials_[n]
110 -= alpha_div_sum * (mu_dbl - y_dbl) / lambda_dbl + inv_sum;
112 ops_partials.
edge4_.partials_[n] += inv_alpha[n] - log1p_scaled_diff[n];
114 return ops_partials.
build(logp);
117 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
120 const T_shape& alpha) {
121 return pareto_type_2_lpdf<false>(y, mu, lambda, alpha);
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.
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.
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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.
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lpdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
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_
fvar< T > log1p(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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_