1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_LOG_HPP
21 #include <boost/math/special_functions/digamma.hpp>
22 #include <boost/random/negative_binomial_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
30 template <
bool propto,
32 typename T_log_location,
typename T_precision>
33 typename return_type<T_log_location, T_precision>::type
35 const T_log_location& eta,
36 const T_precision& phi) {
41 static const char*
function(
"stan::prob::neg_binomial_2_log_log");
48 T_partials_return logp(0.0);
53 "Failures variable", n,
54 "Log location parameter", eta,
55 "Precision parameter", phi);
69 operands_and_partials(eta, phi);
75 for (
size_t i = 0, size =
length(eta); i <
size; ++i)
79 for (
size_t i = 0, size =
length(phi); i <
size; ++i)
84 for (
size_t i = 0, size =
length(phi); i <
size; ++i)
85 log_phi[i] =
log(phi__[i]);
88 logsumexp_eta_logphi(len_ep);
89 for (
size_t i = 0; i < len_ep; ++i)
90 logsumexp_eta_logphi[i] =
log_sum_exp(eta__[i], log_phi[i]);
94 for (
size_t i = 0; i < len_np; ++i)
95 n_plus_phi[i] = n_vec[i] + phi__[i];
97 for (
size_t i = 0; i <
size; i++) {
99 logp -=
lgamma(n_vec[i] + 1.0);
103 logp -= (n_plus_phi[i])*logsumexp_eta_logphi[i];
105 logp += n_vec[i]*eta__[i];
107 logp +=
lgamma(n_plus_phi[i]);
110 operands_and_partials.
d_x1[i]
111 += n_vec[i] - n_plus_phi[i]
112 / (phi__[i]/
exp(eta__[i]) + 1.0);
114 operands_and_partials.
d_x2[i]
115 += 1.0 - n_plus_phi[i]/(
exp(eta__[i]) + phi__[i])
116 + log_phi[i] - logsumexp_eta_logphi[i] -
digamma(phi__[i])
119 return operands_and_partials.
value(logp);
122 template <
typename T_n,
123 typename T_log_location,
typename T_precision>
127 const T_log_location& eta,
128 const T_precision& phi) {
129 return neg_binomial_2_log_log<false>(n, eta, phi);
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > log(const fvar< T > &x)
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
return_type< T_log_location, T_precision >::type neg_binomial_2_log_log(const T_n &n, const T_log_location &eta, const T_precision &phi)
fvar< T > log_sum_exp(const std::vector< fvar< T > > &v)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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 > exp(const fvar< T > &x)
This class builds partial derivatives with respect to a set of operands.
size_t max_size(const T1 &x1, const T2 &x2)
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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.
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.
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)