1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP
26 template <
typename T_n,
typename T_shape,
28 typename return_type<T_shape, T_inv_scale>::type
30 const T_inv_scale& beta) {
31 static const char*
function(
"stan::math::neg_binomial_cdf");
43 T_partials_return P(1.0);
49 "Failures variable", n,
50 "Shape parameter", alpha,
51 "Inverse scale parameter", beta);
67 operands_and_partials(alpha, beta);
73 return operands_and_partials.
to_var(0.0, alpha, beta);
78 T_partials_return, T_shape>
79 digamma_alpha_vec(stan::length(alpha));
82 T_partials_return, T_shape>
83 digamma_sum_vec(stan::length(alpha));
87 const T_partials_return n_dbl =
value_of(n_vec[i]);
88 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
90 digamma_alpha_vec[i] =
digamma(alpha_dbl);
91 digamma_sum_vec[i] =
digamma(n_dbl + alpha_dbl + 1);
95 for (
size_t i = 0; i <
size; i++) {
99 return operands_and_partials.
to_var(1.0, alpha, beta);
101 const T_partials_return n_dbl =
value_of(n_vec[i]);
102 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
103 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
105 const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
106 const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
107 * (1.0 + beta_dbl) );
109 const T_partials_return P_i =
110 inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
115 operands_and_partials.
d_x1[i]
117 digamma_alpha_vec[i],
118 digamma_sum_vec[i]) / P_i;
122 operands_and_partials.
d_x2[i] +=
123 inc_beta_ddz(alpha_dbl, n_dbl + 1.0, p_dbl) * d_dbl / P_i;
128 operands_and_partials.
d_x1[i] *= P;
133 operands_and_partials.
d_x2[i] *= P;
136 return operands_and_partials.
to_var(P, alpha, beta);
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.
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)
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
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)