ghyp: mean-vcov-skew-kurt-methods – R documentation

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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 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

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)

ghyp

Generalized Hyperbolic Distribution and Its Special Cases

v1.6.1

GPL (>= 2)

Authors

Marc Weibel, David Luethi, Wolfgang Breymann

Initial release

2020-04-27