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 #include <boost/math/special_functions/digamma.hpp>
25 #include <boost/random/negative_binomial_distribution.hpp>
26 #include <boost/random/variate_generator.hpp>
34 template <
typename T_n,
typename T_location,
36 typename return_type<T_location, T_precision>::type
39 const T_precision& phi) {
40 static const char*
function(
"stan::prob::neg_binomial_2_cdf");
54 T_partials_return P(1.0);
62 "Location parameter", mu,
63 "Precision Parameter", phi);
79 operands_and_partials(mu, phi);
85 return operands_and_partials.
to_var(0.0, mu, phi);
90 T_partials_return, T_precision>
91 digamma_phi_vec(stan::length(phi));
94 T_partials_return, T_precision>
95 digamma_sum_vec(stan::length(phi));
99 const T_partials_return n_dbl =
value_of(n_vec[i]);
100 const T_partials_return phi_dbl =
value_of(phi_vec[i]);
102 digamma_phi_vec[i] =
digamma(phi_dbl);
103 digamma_sum_vec[i] =
digamma(n_dbl + phi_dbl + 1);
107 for (
size_t i = 0; i <
size; i++) {
111 return operands_and_partials.
to_var(1.0, mu, phi);
113 const T_partials_return n_dbl =
value_of(n_vec[i]);
114 const T_partials_return mu_dbl =
value_of(mu_vec[i]);
115 const T_partials_return phi_dbl =
value_of(phi_vec[i]);
117 const T_partials_return p_dbl = phi_dbl / (mu_dbl + phi_dbl);
118 const T_partials_return d_dbl = 1.0 / ((mu_dbl + phi_dbl)
119 * (mu_dbl + phi_dbl));
121 const T_partials_return P_i =
122 inc_beta(phi_dbl, n_dbl + 1.0, p_dbl);
127 operands_and_partials.
d_x1[i] +=
128 -
inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl) * phi_dbl * d_dbl / P_i;
131 operands_and_partials.
d_x2[i]
134 digamma_sum_vec[i]) / P_i
136 * mu_dbl * d_dbl / P_i;
142 operands_and_partials.
d_x1[i] *= P;
147 operands_and_partials.
d_x2[i] *= P;
150 return operands_and_partials.
to_var(P, mu, phi);
return_type< T_location, T_precision >::type neg_binomial_2_cdf(const T_n &n, const T_location &mu, const T_precision &phi)
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
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.
size_t length(const std::vector< T > &x)
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)
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.
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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)
A variable implementation that stores operands and derivatives with respect to the variable...
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.
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)