momRecursion | R Documentation |
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,\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.
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 = |
lmin |
The minimum of |
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")
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.