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<c3><bc>rtz and Tran (2008). See Details for the formula.

Usage

  momRecursion(order = 12, printMatrix = FALSE)

Arguments

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<c3><bc>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

Author(s)

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

References

Scott, D. J., W<c3><bc>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")

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'license()' or 'licence()' for distribution details.

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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GeneralizedHyperbolic)
Loading required package: DistributionUtils
Loading required package: RUnit
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GeneralizedHyperbolic/momRecursion.Rd_%03d_medium.png", width=480, height=480)
> ### Name: momRecursion
> ### Title: Computes the moment coefficients recursively for generalized
> ###   hyperbolic and related distributions
> ### Aliases: momRecursion
> ### Keywords: distribution
> 
> ### ** Examples
> 
>   momRecursion(order = 12)
$a
 l = 6  l = 7  l = 8  l = 9 l = 10 l = 11 l = 12 
 10395  62370  51975  13860   1485     66      1 

$L
[1]  6  7  8  9 10 11 12

$M
[1]  0  2  4  6  8 10 12

$lmin
[1] 6

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

           l = 1 l = 2 l = 3 l = 4 l = 5 l = 6 l = 7 l = 8 l = 9 l = 10 l = 11
order = 1      1     0     0     0     0     0     0     0     0      0      0
order = 2      1     1     0     0     0     0     0     0     0      0      0
order = 3      0     3     1     0     0     0     0     0     0      0      0
order = 4      0     3     6     1     0     0     0     0     0      0      0
order = 5      0     0    15    10     1     0     0     0     0      0      0
order = 6      0     0    15    45    15     1     0     0     0      0      0
order = 7      0     0     0   105   105    21     1     0     0      0      0
order = 8      0     0     0   105   420   210    28     1     0      0      0
order = 9      0     0     0     0   945  1260   378    36     1      0      0
order = 10     0     0     0     0   945  4725  3150   630    45      1      0
order = 11     0     0     0     0     0 10395 17325  6930   990     55      1
order = 12     0     0     0     0     0 10395 62370 51975 13860   1485     66
           l = 12
order = 1       0
order = 2       0
order = 3       0
order = 4       0
order = 5       0
order = 6       0
order = 7       0
order = 8       0
order = 9       0
order = 10      0
order = 11      0
order = 12      1

$a
 l = 6  l = 7  l = 8  l = 9 l = 10 l = 11 l = 12 
 10395  62370  51975  13860   1485     66      1 

$L
[1]  6  7  8  9 10 11 12

$M
[1]  0  2  4  6  8 10 12

$lmin
[1] 6

> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>