log_gamma_q_dgamma()

template<typename T_a , typename T_z >

std::pair< return_type_t< T_a, T_z >, return_type_t< T_a, T_z > > stan::math::log_gamma_q_dgamma ( const T_a &  a, const T_z &  z, double  precision = internal::LOG_Q_GAMMA_CF_PRECISION, int  max_steps = 250  )

inline

Compute log(Q(a,z)) and its gradient with respect to a using continued fraction expansion, where Q(a,z) = Gamma(a,z) / Gamma(a) is the regularized upper incomplete gamma function.

This uses a continued fraction representation for numerical stability when computing the upper incomplete gamma function in log space, along with analytical gradient computation.

Template Parameters

T_a	type of the shape parameter
T_z	type of the value parameter

Parameters

a	shape parameter (must be positive)
z	value parameter (must be non-negative)
precision	convergence threshold, default of sqrt(machine_epsilon)
max_steps	maximum iterations for continued fraction

Returns

structure containing log(Q(a,z)) and d/da log(Q(a,z))

Definition at line 95 of file log_gamma_q_dgamma.hpp.