1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_CDF_HPP 24 template <
typename T_n,
typename T_location,
29 const T_precision& phi) {
30 static const char*
function(
"neg_binomial_2_cdf");
35 T_partials_return P(1.0);
46 "Location parameter", mu,
47 "Precision Parameter", phi);
55 operands_and_partials(mu, phi);
61 return operands_and_partials.
value(0.0);
65 T_partials_return, T_precision>
66 digamma_phi_vec(stan::length(phi));
69 T_partials_return, T_precision>
70 digamma_sum_vec(stan::length(phi));
74 const T_partials_return n_dbl =
value_of(n_vec[i]);
75 const T_partials_return phi_dbl =
value_of(phi_vec[i]);
77 digamma_phi_vec[i] =
digamma(phi_dbl);
78 digamma_sum_vec[i] =
digamma(n_dbl + phi_dbl + 1);
82 for (
size_t i = 0; i <
size; i++) {
86 return operands_and_partials.
value(1.0);
88 const T_partials_return n_dbl =
value_of(n_vec[i]);
89 const T_partials_return mu_dbl =
value_of(mu_vec[i]);
90 const T_partials_return phi_dbl =
value_of(phi_vec[i]);
92 const T_partials_return p_dbl = phi_dbl / (mu_dbl + phi_dbl);
93 const T_partials_return d_dbl = 1.0 / ((mu_dbl + phi_dbl)
94 * (mu_dbl + phi_dbl));
96 const T_partials_return P_i =
97 inc_beta(phi_dbl, n_dbl + 1.0, p_dbl);
102 operands_and_partials.
d_x1[i] +=
103 -
inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl) * phi_dbl * d_dbl / P_i;
106 operands_and_partials.
d_x2[i]
109 digamma_sum_vec[i]) / P_i
111 * mu_dbl * d_dbl / P_i;
117 operands_and_partials.
d_x1[i] *= P;
122 operands_and_partials.
d_x2[i] *= P;
125 return operands_and_partials.
value(P);
VectorView< T_return_type, false, true > d_x2
return_type< T_location, T_precision >::type neg_binomial_2_cdf(const T_n &n, const T_location &mu, const T_precision &phi)
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.
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
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.
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 check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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.
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
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.