# momRecursion: Computes the moment coefficients recursively for generalized... In HyperbolicDist: The Hyperbolic Distribution

 momRecursion R Documentation

## Computes the moment coefficients recursively for generalized hyperbolic and related distributions

### Description

This function computes all of the moments coefficients by recursion based on Scott, Würtz and Tran (2008). See Details for the formula.

### Usage

  momRecursion(order = 12, printMatrix = FALSE)


### Arguments

 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?

### Details

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.

### Value

 a The non-zero moment coefficients for the specified order. l Integers from (order+1)/2 to order. It is used when computing the moment coefficients and the mu moments. M The common term used when computing mu moments for generalized hyperbolic and related distributions, M = 2\ell - k, k=order lmin The minimum of \ell, which is equal to (order+1)/2.

### Author(s)

David Scott d.scott@auckland.ac.nz, Christine Yang Dong c.dong@auckland.ac.nz

### References

Scott, D. J., Würtz, D. and Tran, T. T. (2008) Moments of the Generalized Hyperbolic Distribution. Preprint.

### Examples

  momRecursion(order = 12)

#print out the matrix
momRecursion(order = 12, "true")


HyperbolicDist documentation built on Nov. 26, 2023, 9:07 a.m.