ghyp (version 1.6.5)

ghyp.moment: Compute moments of generalized hyperbolic distributions

Description

This function computes moments of arbitrary orders of the univariate generalized hyperbolic distribution. The expectation of \(f(X - c)^k\) is calculated. \(f\) can be either the absolute value or the identity. \(c\) can be either zero or \(E(X)\).

Usage

ghyp.moment(object, order = 3:4, absolute = FALSE, central = TRUE, ...)

Value

A vector containing the moments.

Arguments

object

A univarite generalized hyperbolic object inheriting from class ghyp.

order

A vector containing the order of the moments.

absolute

Indicate whether the absolute value is taken or not. If absolute = TRUE then \(E(|X - c|^k)\) is computed. Otherwise \(E((X - c)^k)\). \(c\) depends on the argument central. absolute must be TRUE if order is not integer.

central

If TRUE the moment around the expected value \(E((X - E(X))^k)\) is computed. Otherwise \(E(X^k)\).

...

Arguments passed to integrate.

Author

David Luethi

Details

In general ghyp.moment is based on numerical integration. For the special cases of either a “ghyp”, “hyp” or “NIG” distribution analytic expressions (see References) will be taken if non-absolute and non-centered moments of integer order are requested.

References

Moments of the Generalized Hyperbolic Distribution by David J. Scott, Diethelm Wuertz and Thanh Tam Tran
Working paper, 2008

See Also

mean, vcov, Egig

Examples

  nig.uv <- NIG(alpha.bar = 0.1, mu = 1.1, sigma = 3, gamma = -2)

  # Moments of integer order
  ghyp.moment(nig.uv, order = 1:6)

  # Moments of fractional order
  ghyp.moment(nig.uv, order = 0.2 * 1:20, absolute = TRUE)