hyperb.mean {HyperbolicDist} | R Documentation |
Functions to calculate the mean, variance, and mode of a specific
hyperbolic distribution. R.lambda
and S.lambda
are
functions derived from Bessel functions which are used in the
calculation of the mean and variance.
hyperb.mean(theta) hyperb.var(theta) hyperb.mode(theta) R.lambda(zeta, lambda = 1) S.lambda(zeta, lambda = 1)
theta |
Parameter vector of the hyperbolic distribution |
zeta |
Value of the parameter zeta of the hyperbolic distribution |
lambda |
Parameter related to order of Bessel functions |
hyperb.mean
gives the mean of the hyperbolic distribution,
hyperb.var
the variance, and hyperb.mode
the mode.
The formulae used are as given in Barndorff-Nielsen and Blaesild
(1983), p. 702. The functions R.lambda
and S.lambda
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 parameterisation of the hyperbolic distribution used for this
and other components of the hyperbolic
package is the
pi/zeta one. See hyperb.change.pars
to transfer between
parameterisations.
David Scott d.scott@auckland.ac.nz, Richard Trendall
Barndorff-Nielsen, O. and Blaesild, 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
, hyperb.change.pars
,
besselK
theta <- c(2,2,2,2) hyperb.mean(theta) hyperb.var(theta) hyperb.mode(theta)