1 #ifndef STAN_MATH_PRIM_SCAL_FUN_INC_BETA_DDB_HPP
2 #define STAN_MATH_PRIM_SCAL_FUN_INC_BETA_DDB_HPP
14 T digamma_a, T digamma_ab);
40 T digamma_b, T digamma_ab) {
44 if ((0.1 < z && z <= 0.75 && b > 500)
45 || (0.01 < z && z <= 0.1 && b > 2500)
46 || (0.001 < z && z <= 0.01 && b > 1e5))
47 return -
inc_beta_dda(b, a, 1 - z, digamma_b, digamma_ab);
49 if ((z > 0.75 && a < 500)
50 || (z > 0.9 && a < 2500)
51 || (z > 0.99 && a < 1e5)
53 return -
inc_beta_dda(b, a, 1 - z, digamma_b, digamma_ab);
55 double threshold = 1
e-10;
58 T prefactor = (a + 1) / (a + b);
59 prefactor = prefactor * prefactor * prefactor;
61 T sum_numer = digamma_ab * prefactor;
62 T sum_denom = prefactor;
64 T summand = prefactor * z * (a + b) / (a + 1);
67 digamma_ab += 1.0 / (a + b);
69 while (
fabs(summand) > threshold) {
70 sum_numer += digamma_ab * summand;
73 summand *= (1 + (a + b) / k) * (1 + k) / (1 + (a + 1) / k);
74 digamma_ab += 1.0 / (a + b + k);
80 "did not converge within 100000 iterations",
"",
"");
84 * (
log(1 - z) - digamma_b + sum_numer / sum_denom);
fvar< T > fabs(const fvar< T > &x)
T inc_beta_dda(T a, T b, T z, T digamma_a, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a.
fvar< T > log(const fvar< T > &x)
T inc_beta_ddb(T a, T b, T z, T digamma_b, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to b.
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
void domain_error(const char *function, const char *name, const T &y, const char *msg1, const char *msg2)
Throw a domain error with a consistently formatted message.
double e()
Return the base of the natural logarithm.