a1_pk {qfratio}

Recursion for a_{p,k}

Description

a1_pk() is an internal function to calculate a_{p,k} (a_{r,l} in Hillier et al. 2014; eq. 24), which is used in the calculation of the moment of such a ratio of quadratic forms in normal variables where the denominator matrix is identity.

Usage

a1_pk(L, mu = rep.int(0, n), m = 10L)

Arguments

L

Eigenvalues of the argument matrix; vector of \lambda_i

mu

Mean vector \bm{\mu} for \mathbf{x}

m

Scalar to specify the desired order

Details

This function implements the super-short recursion described in Hillier et al. (2014 eqs. 31–32). Note that w_{r,i} there should be understood as w_{r,l,i} with the index l fixed for each a_{r,l}.

See Also

qfrm_ApIq_int(), in which this function is used (for noncentral cases only)