binomial_ccdf_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CCDF_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_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_bounded.hpp>
#include <stan/math/prim/scal/err/check_finite.hpp>
#include <stan/math/prim/scal/err/check_greater_or_equal.hpp>
#include <stan/math/prim/scal/err/check_less_or_equal.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/inv_logit.hpp>
#include <stan/math/prim/scal/fun/log1m.hpp>
#include <stan/math/prim/scal/fun/log_inv_logit.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
#include <stan/math/prim/scal/fun/lbeta.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/inc_beta.hpp>
#include <boost/random/binomial_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
namespace stan {
namespace math {
template <typename T_n, typename T_N, typename T_prob>
typename return_type<T_prob>::type
binomial_ccdf_log(const T_n& n, const T_N& N, const T_prob& theta) {
static const char* function("binomial_ccdf_log");
typedef typename stan::partials_return_type<T_n, T_N, T_prob>::type
T_partials_return;
if (!(stan::length(n) && stan::length(N) && stan::length(theta)))
return 0.0;
T_partials_return P(0.0);
check_nonnegative(function, "Population size parameter", N);
check_finite(function, "Probability parameter", theta);
check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
check_consistent_sizes(function,
"Successes variable", n,
"Population size parameter", N,
"Probability parameter", theta);
VectorView<const T_n> n_vec(n);
VectorView<const T_N> N_vec(N);
VectorView<const T_prob> theta_vec(theta);
size_t size = max_size(n, N, theta);
using std::exp;
using std::pow;
using std::log;
using std::exp;
OperandsAndPartials<T_prob> operands_and_partials(theta);
// Explicit return for extreme values
// The gradients are technically ill-defined,
// but treated as negative infinity
for (size_t i = 0; i < stan::length(n); i++) {
if (value_of(n_vec[i]) < 0)
return operands_and_partials.value(0.0);
}
for (size_t i = 0; i < size; i++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
return operands_and_partials.value(negative_infinity());
}
const T_partials_return n_dbl = value_of(n_vec[i]);
const T_partials_return N_dbl = value_of(N_vec[i]);
const T_partials_return theta_dbl = value_of(theta_vec[i]);
const T_partials_return betafunc = exp(lbeta(N_dbl-n_dbl, n_dbl+1));
const T_partials_return Pi = 1.0 - inc_beta(N_dbl - n_dbl, n_dbl + 1,
1 - theta_dbl);
P += log(Pi);
if (!is_constant_struct<T_prob>::value)
operands_and_partials.d_x1[i] += pow(theta_dbl, n_dbl)
* pow(1-theta_dbl, N_dbl-n_dbl-1) / betafunc / Pi;
}
return operands_and_partials.value(P);
}
}
}
#endif
stan::math::check_finite
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
Definition: check_finite.hpp:57
stan::math::check_bounded
void check_bounded(const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high)
Check if the value is between the low and high values, inclusively.
Definition: check_bounded.hpp:90
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::lbeta
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
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
binomial_coefficient_log.hpp
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
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
log_inv_logit.hpp
stan::math::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
check_less_or_equal.hpp
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
log1m.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
check_bounded.hpp
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
check_finite.hpp
lbeta.hpp
inc_beta.hpp
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
check_greater_or_equal.hpp
value_of.hpp
inv_logit.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::binomial_ccdf_log
return_type< T_prob >::type binomial_ccdf_log(const T_n &n, const T_N &N, const T_prob &theta)
Definition: binomial_ccdf_log.hpp:32
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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