ghypScale function

Rescale a generalized hyperbolic distribution

Given a specific mean and standard deviation will rescale any given generalized hyperbolic distribution to have the same shape but the specified mean and standard deviation. Can be used to standardize a generalized hyperbolic distribution to have mean zero and standard deviation one.

ghypScale(newMean, newSD,
          mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
          param = c(mu, delta, alpha, beta, lambda))

Arguments

• newMean: Numeric. The required mean of the rescaled distribution.

• newSD: Numeric. The required standard deviation of the rescaled distribution.

• mu: Numeric. Location parameter $mu$ of the starting distribution, default is0.

• delta: Numeric. Scale parameter $delta$ of the starting distribution, default is 1.

• alpha: Numeric. Tail parameter $alpha$ of the starting distribution, default is 1.

• beta: Numeric. Skewness parameter $beta$ of the starting distribution, default is 0.

• lambda: Numeric. Shape parameter $lambda$ of the starting distribution, default is 1.

• param: Numeric. Specifying the parameters of the starting distribution as a vector of the form

  c(mu,delta,alpha,beta,lambda).

Returns

A numerical vector of length 5 giving the value of the parameters in the rescaled generalized hyperbolic distribution in the usual ($alpha, beta$) parameterization.

Author(s)

David Scott d.scott@auckland.ac.nz

Examples

param <- c(2,10,0.1,0.07,-0.5) # a normal inverse Gaussian
ghypMean(param = param)
ghypVar(param = param)
## convert to standardized parameters
(newParam <- ghypScale(0, 1, param = param))
ghypMean(param = newParam)
ghypVar(param = newParam)

## try some other mean and sd
(newParam <- ghypScale(1, 1, param = param))
ghypMean(param = newParam)
sqrt(ghypVar(param = newParam))
(newParam <- ghypScale(10, 2, param = param))
ghypMean(param = newParam)
sqrt(ghypVar(param = newParam))