1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_LOG_HPP
4 #include <boost/math/special_functions/digamma.hpp>
5 #include <boost/random/negative_binomial_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
29 template <
typename T_n,
typename T_shape,
31 typename return_type<T_shape, T_inv_scale>::type
33 const T_inv_scale& beta) {
34 static const char*
function(
"stan::math::neg_binomial_cdf_log");
48 T_partials_return P(0.0);
54 "Failures variable", n,
55 "Shape parameter", alpha,
56 "Inverse scale parameter", beta);
76 operands_and_partials(alpha, beta);
88 T_partials_return, T_shape>
89 digammaN_vec(stan::length(alpha));
91 T_partials_return, T_shape>
92 digammaAlpha_vec(stan::length(alpha));
94 T_partials_return, T_shape>
95 digammaSum_vec(stan::length(alpha));
99 const T_partials_return n_dbl =
value_of(n_vec[i]);
100 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
102 digammaN_vec[i] =
digamma(n_dbl + 1);
103 digammaAlpha_vec[i] =
digamma(alpha_dbl);
104 digammaSum_vec[i] =
digamma(n_dbl + alpha_dbl + 1);
108 for (
size_t i = 0; i <
size; i++) {
112 return operands_and_partials.
to_var(0.0, alpha, beta);
114 const T_partials_return n_dbl =
value_of(n_vec[i]);
115 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
116 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
117 const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
118 const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
119 * (1.0 + beta_dbl) );
120 const T_partials_return Pi =
inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
121 const T_partials_return beta_func =
exp(
lbeta(n_dbl + 1, alpha_dbl));
127 T_partials_return g1 = 0;
128 T_partials_return g2 = 0;
136 operands_and_partials.
d_x1[i] += g1 / Pi;
139 operands_and_partials.
d_x2[i] += d_dbl *
pow(1-p_dbl, n_dbl)
140 *
pow(p_dbl, alpha_dbl-1) / beta_func / Pi;
143 return operands_and_partials.
to_var(P, alpha, beta);
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)
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)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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)
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)
fvar< T > exp(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
fvar< T > pow(const fvar< T > &x1, const fvar< T > &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...
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
double negative_infinity()
Return negative infinity.
fvar< T > digamma(const fvar< T > &x)