1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LCDF_HPP 44 template <
typename T_n,
typename T_N,
45 typename T_size1,
typename T_size2>
48 const T_size2& beta) {
49 static const char*
function(
"beta_binomial_lcdf");
58 T_partials_return P(0.0);
62 "First prior sample size parameter", alpha);
64 "Second prior sample size parameter", beta);
66 "Successes variable", n,
67 "Population size parameter", N,
68 "First prior sample size parameter", alpha,
69 "Second prior sample size parameter", beta);
82 operands_and_partials(alpha, beta);
91 for (
size_t i = 0; i <
size; i++) {
98 const T_partials_return n_dbl =
value_of(n_vec[i]);
99 const T_partials_return N_dbl =
value_of(N_vec[i]);
100 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
101 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
103 const T_partials_return mu = alpha_dbl + n_dbl + 1;
104 const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
107 F =
F32((T_partials_return)1, mu, -N_dbl + n_dbl + 1, n_dbl + 2,
108 1 - nu, (T_partials_return)1);
110 T_partials_return C =
lgamma(nu) -
lgamma(N_dbl - n_dbl);
112 C +=
lgamma(N_dbl + 2) -
lgamma(N_dbl + alpha_dbl + beta_dbl);
115 C *= F /
exp(
lbeta(alpha_dbl, beta_dbl));
118 const T_partials_return Pi = 1 - C;
122 T_partials_return dF[6];
123 T_partials_return digammaOne = 0;
124 T_partials_return digammaTwo = 0;
128 digammaTwo =
digamma(alpha_dbl + beta_dbl);
129 grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
130 n_dbl + 2, 1 - nu, (T_partials_return)1);
133 const T_partials_return g
134 = - C * (
digamma(mu) - digammaOne + dF[1] / F
135 -
digamma(alpha_dbl) + digammaTwo);
136 operands_and_partials.
d_x1[i] += g / Pi;
139 const T_partials_return g
142 operands_and_partials.
d_x2[i] += g / Pi;
146 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 F32(const T &a1, const T &a2, const T &a3, const T &b1, const T &b2, const T &z, double precision=1e-6, int max_steps=1e5)
Hypergeometric function (3F2).
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
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)
This class builds partial derivatives with respect to a set of operands.
size_t max_size(const T1 &x1, const T2 &x2)
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
void grad_F32(T *g, const T &a1, const T &a2, const T &a3, const T &b1, const T &b2, const T &z, const T &precision=1e-6, int max_steps=1e5)
Gradients of the hypergeometric function, 3F2.
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.
return_type< T_size1, T_size2 >::type beta_binomial_lcdf(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Returns the log CDF of the Beta-Binomial distribution with given population size, prior success...