1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_LOG_HPP
25 template <
typename T_n,
typename T_N,
26 typename T_size1,
typename T_size2>
27 typename return_type<T_size1, T_size2>::type
29 const T_size2& beta) {
30 static const char*
function(
"stan::math::beta_binomial_cdf_log");
46 T_partials_return P(0.0);
51 "First prior sample size parameter", alpha);
53 "Second prior sample size parameter", beta);
55 "Successes variable", n,
56 "Population size parameter", N,
57 "First prior sample size parameter", alpha,
58 "Second prior sample size parameter", beta);
76 operands_and_partials(alpha, beta);
86 for (
size_t i = 0; i <
size; i++) {
93 const T_partials_return n_dbl =
value_of(n_vec[i]);
94 const T_partials_return N_dbl =
value_of(N_vec[i]);
95 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
96 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
98 const T_partials_return mu = alpha_dbl + n_dbl + 1;
99 const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
104 (T_partials_return)1);
106 T_partials_return C =
lgamma(nu) -
lgamma(N_dbl - n_dbl);
108 C +=
lgamma(N_dbl + 2) -
lgamma(N_dbl + alpha_dbl + beta_dbl);
111 C *= F /
exp(
lbeta(alpha_dbl, beta_dbl));
114 const T_partials_return Pi = 1 - C;
118 T_partials_return dF[6];
119 T_partials_return digammaOne = 0;
120 T_partials_return digammaTwo = 0;
124 digammaTwo =
digamma(alpha_dbl + beta_dbl);
126 n_dbl + 2, 1 - nu, (T_partials_return)1);
129 const T_partials_return g
130 = - C * (
digamma(mu) - digammaOne + dF[1] / F
131 -
digamma(alpha_dbl) + digammaTwo);
132 operands_and_partials.
d_x1[i] += g / Pi;
135 const T_partials_return g
138 operands_and_partials.
d_x2[i] += g / Pi;
142 return operands_and_partials.
to_var(P, alpha, beta);
fvar< T > lgamma(const fvar< T > &x)
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)
return_type< T_size1, T_size2 >::type beta_binomial_cdf_log(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
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...
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)
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)
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.
T F32(T a, T b, T c, T d, T e, T z, T precision=1e-6)
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.
double negative_infinity()
Return negative infinity.
fvar< T > digamma(const fvar< T > &x)