ghyp: ghyp.moment – R documentation

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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, ...)

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`.

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.

Value

A vector containing the moments.

Author(s)

David Luethi

References

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

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)

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