pareto_ccdf_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_CCDF_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_PARETO_CCDF_LOG_HPP
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_greater_or_equal.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_not_nan.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <boost/random/exponential_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
#include <limits>
namespace stan {
namespace math {
template <typename T_y, typename T_scale, typename T_shape>
typename return_type<T_y, T_scale, T_shape>::type
pareto_ccdf_log(const T_y& y, const T_scale& y_min,
const T_shape& alpha) {
typedef typename stan::partials_return_type<T_y, T_scale, T_shape>::type
T_partials_return;
if ( !( stan::length(y) && stan::length(y_min) && stan::length(alpha) ) )
return 0.0;
static const char* function("pareto_ccdf_log");
using std::log;
using std::exp;
T_partials_return P(0.0);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_positive_finite(function, "Scale parameter", y_min);
check_positive_finite(function, "Shape parameter", alpha);
check_consistent_sizes(function,
"Random variable", y,
"Scale parameter", y_min,
"Shape parameter", alpha);
VectorView<const T_y> y_vec(y);
VectorView<const T_scale> y_min_vec(y_min);
VectorView<const T_shape> alpha_vec(alpha);
size_t N = max_size(y, y_min, alpha);
OperandsAndPartials<T_y, T_scale, T_shape>
operands_and_partials(y, y_min, alpha);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++) {
if (value_of(y_vec[i]) < value_of(y_min_vec[i]))
return operands_and_partials.value(0.0);
}
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
return operands_and_partials.value(negative_infinity());
}
const T_partials_return log_dbl = log(value_of(y_min_vec[n])
/ value_of(y_vec[n]));
const T_partials_return y_min_inv_dbl = 1.0 / value_of(y_min_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
P += alpha_dbl * log_dbl;
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] -= alpha_dbl * y_min_inv_dbl
* exp(log_dbl);
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x2[n] += alpha_dbl * y_min_inv_dbl;
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x3[n] += log_dbl;
}
return operands_and_partials.value(P);
}
}
}
#endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
check_positive_finite.hpp
stan
Definition: log_sum_exp.hpp:8
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::math::pareto_ccdf_log
return_type< T_y, T_scale, T_shape >::type pareto_ccdf_log(const T_y &y, const T_scale &y_min, const T_shape &alpha)
Definition: pareto_ccdf_log.hpp:25
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
stan::math::OperandsAndPartials::value
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
Definition: OperandsAndPartials.hpp:67
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
stan::math::check_nonnegative
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
Definition: check_nonnegative.hpp:61
stan::return_type::type
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
Definition: return_type.hpp:27
multiply_log.hpp
check_nonnegative.hpp
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:13
stan::math::check_positive_finite
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
Definition: check_positive_finite.hpp:26
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::check_not_nan
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
Definition: check_not_nan.hpp:57
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:40
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
partials_return_type.hpp
OperandsAndPartials.hpp
constants.hpp
check_greater_or_equal.hpp
value_of.hpp
stan::VectorView
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[].
Definition: VectorView.hpp:48
stan::math::check_consistent_sizes
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.
Definition: check_consistent_sizes.hpp:30
stan::partials_return_type::type
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
Definition: partials_return_type.hpp:26
check_consistent_sizes.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130

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