momRecursion | R Documentation |
This function computes all of the moments coefficients by recursion based on Scott, W<fc>rtz 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, W<fc>rtz 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., W<fc>rtz, 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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