log_mix() [10/12]

template<typename T_theta , typename T_lam , require_any_vector_t< T_theta, T_lam > * = nullptr>

return_type_t< T_theta, T_lam > stan::math::log_mix	(	const T_theta &	theta,
		const T_lam &	lambda
	)

Return the log mixture density with specified mixing proportions and log densities.

\[ \frac{\partial }{\partial p_x} \log\left(\exp^{\log\left(p_1\right)+d_1}+\cdot\cdot\cdot+ \exp^{\log\left(p_n\right)+d_n}\right) =\frac{e^{d_x}}{e^{d_1}p_1+\cdot\cdot\cdot+e^{d_m}p_m} \]

\[ \frac{\partial }{\partial d_x} \log\left(\exp^{\log\left(p_1\right)+d_1}+\cdot\cdot\cdot+ \exp^{\log\left(p_n\right)+d_n}\right) =\frac{e^{d_x}p_x}{e^{d_1}p_1+\cdot\cdot\cdot+e^{d_m}p_m} \]

Template Parameters

T_theta	Type of theta. This can be a scalar, std vector or row/column vector.
T_lam	Type of lambda. This can be a scalar, std vector or row/column vector.

Parameters

theta	std/row/col vector of mixing proportions in [0, 1].
lambda	std/row/col vector of log densities.

Returns

log mixture of densities in specified proportion

Definition at line 77 of file log_mix.hpp.