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))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 |
A numerical vector of length 5 giving the value of the parameters in the rescaled generalized hyperbolic distribution in the usual (alpha, beta) parameterization.
David Scott d.scott@auckland.ac.nz
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))
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