This function computes all of the moments coefficients by recursion based on Scott, Würtz and Tran (2008). See Details for the formula.
momRecursion(order = 12, printMatrix = FALSE)
The non-zero moment coefficients for the specified order.
Integers from (order+1)/2 to order. It is used when
computing the moment coefficients and the mu moments.
The common term used when computing mu moments for generalized
hyperbolic and related distributions, M = \(2\ell - k\),
\(k\)=order
The minimum of \(\ell\), which is equal to
(order+1)/2.
Numeric. The order of the moment coefficients to be calculated. Not permitted to be a vector. Must be a positive whole number except for moments about zero.
Logical. Should the coefficients matrix be printed?
David Scott d.scott@auckland.ac.nz, Christine Yang Dong c.dong@auckland.ac.nz
The moment coefficients recursively as \(a_{1,1}=1\) and
$$a_{k,\ell} = a_{k-1, \ell-1} + (2 \ell - k + 1) a_{k-1, \ell}$$ with
\(a_{k,\ell} = 0\) for \(\ell<\lfloor(k+1)/2\rfloor\) or \(\ell>k\)
where \(k\) = order, \(\ell\) is equal to the integers from
\((k+1)/2\) to \(k\).
This formula is given in Scott, Würtz and Tran (2008, working paper).
The function also calculates M which is equal to \(2\ell - k\). It is a common term which will appear in the formulae for calculating moments of generalized hyperbolic and related distributions.
Scott, D. J., Würtz, D. and Tran, T. T. (2008) Moments of the Generalized Hyperbolic Distribution. Preprint.
momRecursion(order = 12)
#print out the matrix
momRecursion(order = 12, "true")
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