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
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 <
bool propto,
31 typename T_log_location,
typename T_precision>
32 typename return_type<T_log_location, T_precision>::type
34 const T_log_location& eta,
35 const T_precision& phi) {
40 static const char*
function(
"stan::prob::neg_binomial_2_log_log");
55 T_partials_return logp(0.0);
60 "Failures variable", n,
61 "Log location parameter", eta,
62 "Precision parameter", phi);
82 operands_and_partials(eta, phi);
88 for (
size_t i = 0, size =
length(eta); i <
size; ++i)
92 for (
size_t i = 0, size =
length(phi); i <
size; ++i)
98 for (
size_t i = 0, size =
length(phi); i <
size; ++i)
99 log_phi[i] =
log(phi__[i]);
102 logsumexp_eta_logphi(len_ep);
103 for (
size_t i = 0; i < len_ep; ++i)
104 logsumexp_eta_logphi[i] =
log_sum_exp(eta__[i], log_phi[i]);
108 for (
size_t i = 0; i < len_np; ++i)
109 n_plus_phi[i] = n_vec[i] + phi__[i];
111 for (
size_t i = 0; i <
size; i++) {
113 logp -=
lgamma(n_vec[i] + 1.0);
117 logp -= (n_plus_phi[i])*logsumexp_eta_logphi[i];
119 logp += n_vec[i]*eta__[i];
121 logp +=
lgamma(n_plus_phi[i]);
124 operands_and_partials.
d_x1[i]
125 += n_vec[i] - n_plus_phi[i]
126 / (phi__[i]/
exp(eta__[i]) + 1.0);
128 operands_and_partials.
d_x2[i]
129 += 1.0 - n_plus_phi[i]/(
exp(eta__[i]) + phi__[i])
130 + log_phi[i] - logsumexp_eta_logphi[i] -
digamma(phi__[i])
133 return operands_and_partials.
to_var(logp, eta, phi);
136 template <
typename T_n,
137 typename T_log_location,
typename T_precision>
141 const T_log_location& eta,
142 const T_precision& phi) {
143 return neg_binomial_2_log_log<false>(n, eta, phi);
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)
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)
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)
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
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 > 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)
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)
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)