1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_LOG_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_LOG_HPP 21 #include <boost/math/special_functions/digamma.hpp> 22 #include <boost/random/negative_binomial_distribution.hpp> 23 #include <boost/random/variate_generator.hpp> 30 template <
typename T_n,
typename T_shape,
34 const T_inv_scale& beta) {
35 static const char*
function(
"neg_binomial_cdf_log");
43 T_partials_return P(0.0);
48 "Failures variable", n,
49 "Shape parameter", alpha,
50 "Inverse scale parameter", beta);
63 operands_and_partials(alpha, beta);
73 T_partials_return, T_shape>
74 digammaN_vec(stan::length(alpha));
76 T_partials_return, T_shape>
77 digammaAlpha_vec(stan::length(alpha));
79 T_partials_return, T_shape>
80 digammaSum_vec(stan::length(alpha));
84 const T_partials_return n_dbl =
value_of(n_vec[i]);
85 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
87 digammaN_vec[i] =
digamma(n_dbl + 1);
88 digammaAlpha_vec[i] =
digamma(alpha_dbl);
89 digammaSum_vec[i] =
digamma(n_dbl + alpha_dbl + 1);
93 for (
size_t i = 0; i <
size; i++) {
97 return operands_and_partials.
value(0.0);
99 const T_partials_return n_dbl =
value_of(n_vec[i]);
100 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
101 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
102 const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
103 const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
104 * (1.0 + beta_dbl) );
105 const T_partials_return Pi =
inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
106 const T_partials_return beta_func =
exp(
lbeta(n_dbl + 1, alpha_dbl));
111 T_partials_return g1 = 0;
112 T_partials_return g2 = 0;
120 operands_and_partials.
d_x1[i] += g1 / Pi;
123 operands_and_partials.
d_x2[i] += d_dbl *
pow(1-p_dbl, n_dbl)
124 *
pow(p_dbl, alpha_dbl-1) / beta_func / Pi;
127 return operands_and_partials.
value(P);
VectorView< T_return_type, false, true > d_x2
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > log(const fvar< T > &x)
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
return_type< T_shape, T_inv_scale >::type neg_binomial_cdf_log(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void grad_reg_inc_beta(T &g1, T &g2, const T &a, const T &b, const T &z, const T &digammaA, const T &digammaB, const T &digammaSum, const T &betaAB)
Computes the gradients of the regularized incomplete beta function.
fvar< T > exp(const fvar< T > &x)
This class builds partial derivatives with respect to a set of operands.
size_t max_size(const T1 &x1, const T2 &x2)
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
VectorBuilder allocates type T1 values to be used as intermediate values.
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
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[].
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.
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.