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neg_binomial_ccdf_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CCDF_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CCDF_LOG_HPP
#include <boost/math/special_functions/digamma.hpp>
#include <boost/random/negative_binomial_distribution.hpp>
#include <boost/random/variate_generator.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_nonnegative.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/value_of.hpp>
#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/lbeta.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
#include <stan/math/prim/scal/fun/inc_beta.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <cmath>
#include <limits>
namespace stan {
namespace math {
template <typename T_n, typename T_shape,
typename T_inv_scale>
typename return_type<T_shape, T_inv_scale>::type
neg_binomial_ccdf_log(const T_n& n, const T_shape& alpha,
const T_inv_scale& beta) {
static const char* function("stan::math::neg_binomial_ccdf_log");
typedef typename stan::partials_return_type<T_n, T_shape,
T_inv_scale>::type
T_partials_return;
using stan::math::check_positive_finite;
using stan::math::check_nonnegative;
using stan::math::check_consistent_sizes;
using stan::math::include_summand;
// Ensure non-zero arugment lengths
if (!(stan::length(n) && stan::length(alpha) && stan::length(beta)))
return 0.0;
T_partials_return P(0.0);
// Validate arguments
check_positive_finite(function, "Shape parameter", alpha);
check_positive_finite(function, "Inverse scale parameter", beta);
check_consistent_sizes(function,
"Failures variable", n,
"Shape parameter", alpha,
"Inverse scale parameter", beta);
// Wrap arguments in vector views
VectorView<const T_n> n_vec(n);
VectorView<const T_shape> alpha_vec(alpha);
VectorView<const T_inv_scale> beta_vec(beta);
size_t size = max_size(n, alpha, beta);
// Compute vectorized cdf_log and gradient
using stan::math::value_of;
using stan::math::inc_beta;
using stan::math::digamma;
using stan::math::lbeta;
using std::exp;
using std::pow;
using std::log;
using std::exp;
OperandsAndPartials<T_shape, T_inv_scale>
operands_and_partials(alpha, beta);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(n); i++) {
if (value_of(n_vec[i]) < 0)
return operands_and_partials.to_var(0.0, alpha, beta);
}
// Cache a few expensive function calls if alpha is a parameter
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape>
digammaN_vec(stan::length(alpha));
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape>
digammaAlpha_vec(stan::length(alpha));
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape>
digammaSum_vec(stan::length(alpha));
if (!is_constant_struct<T_shape>::value) {
for (size_t i = 0; i < stan::length(alpha); i++) {
const T_partials_return n_dbl = value_of(n_vec[i]);
const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
digammaN_vec[i] = digamma(n_dbl + 1);
digammaAlpha_vec[i] = digamma(alpha_dbl);
digammaSum_vec[i] = digamma(n_dbl + alpha_dbl + 1);
}
}
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]) == std::numeric_limits<int>::max())
return operands_and_partials.to_var(stan::math::negative_infinity(),
alpha, beta);
const T_partials_return n_dbl = value_of(n_vec[i]);
const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
const T_partials_return beta_dbl = value_of(beta_vec[i]);
const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
* (1.0 + beta_dbl) );
const T_partials_return Pi = 1.0 - inc_beta(alpha_dbl, n_dbl + 1.0,
p_dbl);
const T_partials_return beta_func = exp(lbeta(n_dbl + 1, alpha_dbl));
P += log(Pi);
if (!is_constant_struct<T_shape>::value) {
T_partials_return g1 = 0;
T_partials_return g2 = 0;
stan::math::grad_reg_inc_beta(g1, g2, alpha_dbl,
n_dbl + 1, p_dbl,
digammaAlpha_vec[i],
digammaN_vec[i],
digammaSum_vec[i],
beta_func);
operands_and_partials.d_x1[i] -= g1 / Pi;
}
if (!is_constant_struct<T_inv_scale>::value)
operands_and_partials.d_x2[i] -= d_dbl * pow(1-p_dbl, n_dbl)
* pow(p_dbl, alpha_dbl-1) / beta_func / Pi;
}
return operands_and_partials.to_var(P, alpha, beta);
}
}
}
#endif
lgamma.hpp
check_positive_finite.hpp
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:16
digamma.hpp
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
binomial_coefficient_log.hpp
stan::math::OperandsAndPartials::to_var
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
Definition: OperandsAndPartials.hpp:322
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:36
include_summand.hpp
multiply_log.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
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:16
stan::math::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:20
stan::math::neg_binomial_ccdf_log
return_type< T_shape, T_inv_scale >::type neg_binomial_ccdf_log(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
Definition: neg_binomial_ccdf_log.hpp:32
stan::partials_return_type
Definition: partials_return_type.hpp:16
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
stan::math::max
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:21
grad_reg_inc_beta.hpp
stan::VectorBuilder
Definition: VectorBuilder.hpp:61
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Definition: size.hpp:11
stan::math::check_consistent_sizes
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
Definition: check_consistent_sizes.hpp:31
lbeta.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
inc_beta.hpp
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
value_of.hpp
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
stan::math::grad_reg_inc_beta
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
Definition: grad_reg_inc_beta.hpp:14
check_consistent_sizes.hpp
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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