pareto_lpdf.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_LPDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_PARETO_LPDF_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 <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <boost/random/exponential_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
namespace stan {
namespace math {
// Pareto(y|y_m, alpha) [y > y_m; y_m > 0; alpha > 0]
template <bool propto,
typename T_y, typename T_scale, typename T_shape>
typename return_type<T_y, T_scale, T_shape>::type
pareto_lpdf(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
static const char* function("pareto_lpdf");
typedef typename stan::partials_return_type<T_y, T_scale, T_shape>::type
T_partials_return;
using std::log;
if (!(stan::length(y)
&& stan::length(y_min)
&& stan::length(alpha)))
return 0.0;
T_partials_return logp(0.0);
check_not_nan(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);
if (!include_summand<propto, T_y, T_scale, T_shape>::value)
return 0.0;
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);
for (size_t n = 0; n < N; n++) {
if (y_vec[n] < y_min_vec[n])
return LOG_ZERO;
}
OperandsAndPartials<T_y, T_scale, T_shape>
operands_and_partials(y, y_min, alpha);
VectorBuilder<include_summand<propto, T_y, T_shape>::value,
T_partials_return, T_y> log_y(length(y));
if (include_summand<propto, T_y, T_shape>::value) {
for (size_t n = 0; n < length(y); n++)
log_y[n] = log(value_of(y_vec[n]));
}
VectorBuilder<contains_nonconstant_struct<T_y, T_shape>::value,
T_partials_return, T_y> inv_y(length(y));
if (contains_nonconstant_struct<T_y, T_shape>::value) {
for (size_t n = 0; n < length(y); n++)
inv_y[n] = 1 / value_of(y_vec[n]);
}
VectorBuilder<include_summand<propto, T_scale, T_shape>::value,
T_partials_return, T_scale>
log_y_min(length(y_min));
if (include_summand<propto, T_scale, T_shape>::value) {
for (size_t n = 0; n < length(y_min); n++)
log_y_min[n] = log(value_of(y_min_vec[n]));
}
VectorBuilder<include_summand<propto, T_shape>::value,
T_partials_return, T_shape> log_alpha(length(alpha));
if (include_summand<propto, T_shape>::value) {
for (size_t n = 0; n < length(alpha); n++)
log_alpha[n] = log(value_of(alpha_vec[n]));
}
for (size_t n = 0; n < N; n++) {
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
if (include_summand<propto, T_shape>::value)
logp += log_alpha[n];
if (include_summand<propto, T_scale, T_shape>::value)
logp += alpha_dbl * log_y_min[n];
if (include_summand<propto, T_y, T_shape>::value)
logp -= alpha_dbl * log_y[n] + log_y[n];
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] -= alpha_dbl * inv_y[n] + inv_y[n];
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x2[n] += alpha_dbl / value_of(y_min_vec[n]);
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x3[n]
+= 1 / alpha_dbl + log_y_min[n] - log_y[n];
}
return operands_and_partials.value(logp);
}
template <typename T_y, typename T_scale, typename T_shape>
inline
typename return_type<T_y, T_scale, T_shape>::type
pareto_lpdf(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
return pareto_lpdf<false>(y, y_min, alpha);
}
}
}
#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::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
contains_nonconstant_struct.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
stan::math::LOG_ZERO
const double LOG_ZERO
Definition: constants.hpp:172
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:35
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
include_summand.hpp
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::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
VectorBuilder.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
stan::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
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::pareto_lpdf
return_type< T_y, T_scale, T_shape >::type pareto_lpdf(const T_y &y, const T_scale &y_min, const T_shape &alpha)
Definition: pareto_lpdf.hpp:29
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38

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