# 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, W<fc>rtz 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,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.

### 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 = 2l - k, k=`order` `lmin` The minimum of l, 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., W<fc>rtz, 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 March 18, 2022, 6:23 p.m.