VarianceGamma (version 0.4-2)

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)

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 , Christine Yang Dong

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 Podgórski, 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