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qfratio (version 1.1.1)

a1_pk: 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)