1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_CCDF_LOG_HPP
4 #include <boost/math/special_functions/gamma.hpp>
5 #include <boost/random/gamma_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
32 template <
typename T_y,
typename T_scale_succ,
typename T_scale_fail>
33 typename return_type<T_y, T_scale_succ, T_scale_fail>::type
35 const T_scale_fail& beta) {
46 static const char*
function(
"stan::math::beta_cdf");
52 using boost::math::tools::promote_args;
56 T_partials_return ccdf_log(0.0);
65 "First shape parameter", alpha,
66 "Second shape parameter", beta);
75 operands_and_partials(y, alpha, beta);
89 T_partials_return, T_scale_succ, T_scale_fail>
90 digamma_alpha_vec(
max_size(alpha, beta));
93 T_partials_return, T_scale_succ, T_scale_fail>
94 digamma_beta_vec(
max_size(alpha, beta));
97 T_partials_return, T_scale_succ, T_scale_fail>
98 digamma_sum_vec(
max_size(alpha, beta));
101 for (
size_t i = 0; i < N; i++) {
102 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
103 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
105 digamma_alpha_vec[i] =
digamma(alpha_dbl);
106 digamma_beta_vec[i] =
digamma(beta_dbl);
107 digamma_sum_vec[i] =
digamma(alpha_dbl + beta_dbl);
112 for (
size_t n = 0; n < N; n++) {
114 const T_partials_return y_dbl =
value_of(y_vec[n]);
115 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
116 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
117 const T_partials_return betafunc_dbl =
exp(
lbeta(alpha_dbl, beta_dbl));
120 const T_partials_return Pn = 1.0 -
inc_beta(alpha_dbl, beta_dbl, y_dbl);
125 operands_and_partials.
d_x1[n] -=
pow(1-y_dbl, beta_dbl-1)
126 *
pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
128 T_partials_return g1 = 0;
129 T_partials_return g2 = 0;
133 digamma_alpha_vec[n],
139 operands_and_partials.
d_x2[n] -= g1 / Pn;
141 operands_and_partials.
d_x3[n] -= g2 / Pn;
144 return operands_and_partials.
to_var(ccdf_log, y, alpha, beta);
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
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)
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)
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_ccdf_log(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
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 > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
fvar< T > exp(const fvar< T > &x)
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
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_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Return true if y is less or equal to high.
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
fvar< T > pow(const fvar< T > &x1, const fvar< T > &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...
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
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)