vgChangePars: Change Parameterizations of the Variance Gamma Distribution

Description

This function interchanges between the following 4 parameterizations of the variance gamma distribution:

1. $c, σ, θ, ν$

2. $θ, σ, μ, τ$

3. $θ, σ, κ, τ$

4. $λ, α, β, μ$

The first set of parameterizations is given in Seneta (2004). The second and third ones are the parameterizations given in Kotz $e t a l$ . (2001). The last set takes the form of the generalized hyperbolic distribution parameterization. $δ$ is not included since the variance gamma distribution is a limiting case of generalized hyperbolic distribution with $δ$ always equal to 0.

Usage

vgChangePars(from, to, param, noNames = FALSE)

Value

A numerical vector of length 4 representing param in the

to parameterization.

Arguments

from: The set of parameters to change from.
to: The set of parameters to change to.
param: "from" parameter vector consisting of 4 numerical elements.
noNames: Logical. When TRUE, suppresses the parameter names in the output.

Author

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

Details

In the 3 parameterizations, the following must be positive:

1. $σ, ν$

2. $σ, τ$

3. $σ, τ$

4. $λ, α$

In addition in the 4th parameterization, the absolute value of $β$ must be less than $α$ .

References

Seneta, E. (2004). Fitting the variance-gamma model to financial data. J. Appl. Prob., 41A:177--187. Kotz, S, Kozubowski, T. J., and Podgórski, K. (2001). The Laplace Distribution and Generalizations. Birkhauser, Boston, 349 p.

Examples

Run this code

param1 <- c(2,2,1,3)                   # Parameterization 1
param2 <- vgChangePars(1, 2, param1)   # Convert to parameterization 2
param2                                 # Parameterization 2
vgChangePars(2, 1, as.numeric(param2)) # Convert back to parameterization 1

param3 <- c(1,2,0,0.5)                 # Parameterization 3
param1 <- vgChangePars(3, 1, param3)   # Convert to parameterization 1
param1                                 # Parameterization 1
vgChangePars(1, 3, as.numeric(param1)) # Convert back to parameterization 3

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