VarianceGamma (version 0.3-0)

vgChangePars: Change Parameterizations of the Variance Gamma Distribution

Description

This function interchanges between the following 4 parameterizations of the variance gamma distribution: 1. $c, \sigma, \theta, \nu$ 2. $\theta, \sigma, \mu, \tau$ 3. $\theta, \sigma, \kappa, \tau$ 4. $\lambda, \alpha, \beta, \mu$ The first set of parameterizations is given in Seneta (2004). The second and third ones are the parameterizations given in Kotz $et al$. (2001). The last set takes the form of the generalized hyperbolic distribution parameterization. $\delta$ is not included since the variance gamma distribution is a limiting case of generalized hyperbolic distribution with $\delta$ always equal to 0.

Usage

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

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.

Value

• A numerical vector of length 4 representing param in the to parameterization.

Details

In the 3 parameterizations, the following must be positive: 1. $\sigma, \nu$ 2. $\sigma, \tau$ 3. $\sigma, \tau$ 4. $\lambda, \alpha$ In addition in the 4th parameterization, the absolute value of $\beta$ must be less than $\alpha$.

References

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

See Also

dvg, vgMom

Examples

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