ghyp (version 1.6.5)

mean-vcov-skew-kurt-methods: Expected value, variance-covariance, skewness and kurtosis of generalized hyperbolic distributions

Description

The function mean returns the expected value. The function vcov returns the variance in the univariate case and the variance-covariance matrix in the multivariate case. The functions ghyp.skewness and ghyp.kurtosis only work for univariate generalized hyperbolic distributions.

Usage

# S4 method for ghyp
mean(x)
# S4 method for ghyp
vcov(object)
ghyp.skewness(object)
ghyp.kurtosis(object)

Value

Either the expected value, variance, skewness or kurtosis.

Arguments

x, object

An object inheriting from class ghyp.

Author

David Luethi

Details

The functions ghyp.skewness and ghyp.kurtosis are based on the function ghyp.moment. Numerical integration will be used in case a Student.t or variance gamma distribution is submitted.

See Also

ghyp, ghyp-class, Egig to compute the expected value and the variance of the generalized inverse gaussian mixing distribution distributed and its special cases.

Examples

  ## Univariate: Parametric
  vg.dist <- VG(lambda = 1.1, mu = 10, sigma = 10, gamma = 2)
  mean(vg.dist)
  vcov(vg.dist)
  ghyp.skewness(vg.dist)
  ghyp.kurtosis(vg.dist)

  ## Univariate: Empirical
  vg.sim <- rghyp(10000, vg.dist)
  mean(vg.sim)
  var(vg.sim)

  ## Multivariate: Parametric
  vg.dist <- VG(lambda = 0.1, mu = c(55, 33), sigma = diag(c(22, 888)), gamma = 1:2)
  mean(vg.dist)
  vcov(vg.dist)

  ## Multivariate: Empirical
  vg.sim <- rghyp(50000, vg.dist)
  colMeans(vg.sim)
  var(vg.sim)