1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP 19 template <
typename T_n,
typename T_shape,
typename T_inv_scale>
21 const T_n& n,
const T_shape& alpha,
const T_inv_scale&
beta) {
22 static const char*
function =
"neg_binomial_cdf";
29 T_partials_return P(1.0);
34 alpha,
"Inverse scale parameter", beta);
47 return ops_partials.
build(0.0);
51 digamma_alpha_vec(stan::length(alpha));
54 digamma_sum_vec(stan::length(alpha));
58 const T_partials_return n_dbl =
value_of(n_vec[i]);
59 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
61 digamma_alpha_vec[i] =
digamma(alpha_dbl);
62 digamma_sum_vec[i] =
digamma(n_dbl + alpha_dbl + 1);
66 for (
size_t i = 0; i <
size; i++) {
70 return ops_partials.
build(1.0);
72 const T_partials_return n_dbl =
value_of(n_vec[i]);
73 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
74 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
76 const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
77 const T_partials_return d_dbl = 1.0 / ((1.0 + beta_dbl) * (1.0 + beta_dbl));
79 const T_partials_return P_i =
inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
84 ops_partials.
edge1_.partials_[i]
85 +=
inc_beta_dda(alpha_dbl, n_dbl + 1, p_dbl, digamma_alpha_vec[i],
91 ops_partials.
edge2_.partials_[i]
92 +=
inc_beta_ddz(alpha_dbl, n_dbl + 1.0, p_dbl) * d_dbl / P_i;
97 ops_partials.
edge1_.partials_[i] *= P;
102 ops_partials.
edge2_.partials_[i] *= P;
105 return ops_partials.
build(P);
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
return_type< T_shape, T_inv_scale >::type neg_binomial_cdf(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
T inc_beta_dda(T a, T b, T z, T digamma_a, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
T inc_beta_ddz(T a, T b, T z)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z.
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
size_t max_size(const T1 &x1, const T2 &x2)
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
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.
internal::ops_partials_edge< double, Op2 > edge2_
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
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.
internal::ops_partials_edge< double, Op1 > edge1_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.