Description Usage Arguments Value Author(s) References See Also

Functions used to calculate the mean, variance, skewness and kurtosis of a hyperbolic distribution. Not expected to be called directly by users.

1 2 3 4 5 6 7 8 9 | ```
RLambda(zeta, lambda = 1)
SLambda(zeta, lambda = 1)
MLambda(zeta, lambda = 1)
WLambda1(zeta, lambda = 1)
WLambda2(zeta, lambda = 1)
WLambda3(zeta, lambda = 1)
WLambda4(zeta, lambda = 1)
gammaLambda1(hyperbPi, zeta, lambda = 1)
gammaLambda1(hyperbPi, zeta, lambda = 1)
``` |

`hyperbPi` |
Value of the parameter |

`zeta` |
Value of the parameter |

`lambda` |
Parameter related to order of Bessel functions. |

The functions `RLambda`

and `SLambda`

are used in the calculation of the mean and variance. They are
functions of the Bessel functions of the third kind,
implemented in **R** as `besselK`

. The other functions are
used in calculation of higher moments. See Barndorff-Nielsen, O. and
Blaesild, P (1981) for details of the calculations.

The parameterisation of the hyperbolic distribution used for this
and other components of the `HyperbolicDist`

package is the
*(pi,zeta)* one. See `hyperbChangePars`

to
transfer between parameterizations.

David Scott [email protected], Richard Trendall, Thomas Tran

Barndorff-Nielsen, O. and Bl<c3><a6>sild, P (1981).
Hyperbolic distributions and ramifications: contributions to theory
and application.
In *Statistical Distributions in Scientific Work*,
eds., Taillie, C., Patil, G. P., and Baldessari, B. A., Vol. 4,
pp. 19–44. Dordrecht: Reidel.

Barndorff-Nielsen, O. and Bl<c3><a6>sild, P (1983).
Hyperbolic distributions.
In *Encyclopedia of Statistical Sciences*,
eds., Johnson, N. L., Kotz, S. and Read, C. B., Vol. 3,
pp. 700–707. New York: Wiley.

`dhyperb`

,
`hyperbMean`

,`hyperbChangePars`

,
`besselK`

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