Computes the moment coefficients recursively for generalized hyperbolic and related distributions
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)
order |
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. |
printMatrix |
Logical. Should the coefficients matrix be printed? |
The moment coefficients recursively as a_{1,1}=1 and
a_{k,l} = a_{k-1,l=1} + (2l - k + 1) a_{k-1,l}
with
a_k,l = 0 for
l < [(k + 1)/2] or l > k
where k = order, l 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 2l - k. It is a common term which will appear in the formulae for calculating moments of generalized hyperbolic and related distributions.
a |
The non-zero moment coefficients for the specified order. |
l |
Integers from ( |
M |
The common term used when computing mu moments for generalized
hyperbolic and related distributions, M = 2l - k,
k= |
lmin |
The minimum of l, which is equal to
( |
David Scott d.scott@auckland.ac.nz, Christine Yang Dong c.dong@auckland.ac.nz
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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