mean-vcov-skew-kurt-methods {ghyp}R Documentation

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 signature 'ghyp':
mean(x)

## S4 method for signature 'ghyp':
vcov(object)

ghyp.skewness(object)

ghyp.kurtosis(object)

Arguments

x, object An object inheriting from class ghyp.

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.

Value

Either the expected value, variance, skewness or kurtosis.

Author(s)

David Luethi

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)

[Package ghyp version 1.5.0 Index]