1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LCCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LCCDF_HPP 26 template <
typename T_n,
typename T_N,
27 typename T_size1,
typename T_size2>
30 const T_size2& beta) {
31 static const char*
function(
"beta_binomial_lccdf");
40 T_partials_return P(0.0);
44 "First prior sample size parameter", alpha);
46 "Second prior sample size parameter", beta);
48 "Successes variable", n,
49 "Population size parameter", N,
50 "First prior sample size parameter", alpha,
51 "Second prior sample size parameter", beta);
64 operands_and_partials(alpha, beta);
70 return operands_and_partials.
value(0.0);
73 for (
size_t i = 0; i <
size; i++) {
80 const T_partials_return n_dbl =
value_of(n_vec[i]);
81 const T_partials_return N_dbl =
value_of(N_vec[i]);
82 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
83 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
85 const T_partials_return mu = alpha_dbl + n_dbl + 1;
86 const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
88 const T_partials_return F =
F32((T_partials_return)1, mu,
91 (T_partials_return)1);
93 T_partials_return C =
lgamma(nu) -
lgamma(N_dbl - n_dbl);
95 C +=
lgamma(N_dbl + 2) -
lgamma(N_dbl + alpha_dbl + beta_dbl);
98 C *= F /
exp(
lbeta(alpha_dbl, beta_dbl));
101 const T_partials_return Pi = C;
105 T_partials_return dF[6];
106 T_partials_return digammaOne = 0;
107 T_partials_return digammaTwo = 0;
111 digammaTwo =
digamma(alpha_dbl + beta_dbl);
112 grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
113 n_dbl + 2, 1 - nu, (T_partials_return)1);
116 const T_partials_return g
117 = - C * (
digamma(mu) - digammaOne + dF[1] / F
118 -
digamma(alpha_dbl) + digammaTwo);
119 operands_and_partials.
d_x1[i] -= g / Pi;
122 const T_partials_return g
125 operands_and_partials.
d_x2[i] -= g / Pi;
129 return operands_and_partials.
value(P);
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
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)
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)
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > exp(const fvar< T > &x)
return_type< T_size1, T_size2 >::type beta_binomial_lccdf(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
This class builds partial derivatives with respect to a set of operands.
size_t max_size(const T1 &x1, const T2 &x2)
void grad_F32(T *g, T a, T b, T c, T d, T e, T z, T precision=1e-6)
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
T F32(T a, T b, T c, T d, T e, T z, T precision=1e-6)
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[].
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.