a1_pk {qfratio}R Documentation

Recursion for a_{p,k}

Description

a1_pk() is an internal function to calculate ap,ka_{p,k} (ar,la_{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 λi\lambda_i

mu

Mean vector μ\bm{\mu} for x\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 wr,iw_{r,i} there should be understood as wr,l,iw_{r,l,i} with the index ll fixed for each ar,la_{r,l}.

See Also

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


[Package qfratio version 1.1.1 Index]