sn (version 0.4-3)

sn.cumulants: Cumulants of the skew-normal distribution

Description

Cumulants of the skew-normal distribution.

Usage

sn.cumulants(location = 0, scale = 1, shape = 0,  n = 4)
sn.cumulants(dp=, n = 4)

Arguments

location

location parameter (vector)

scale

scale parameter (vector)

shape

shape parameter (vector)

dp

a vector of three elements, whose elements are (location, scale, shape) respectively. If dp is specified, then the individual parameters must not be.

n

a scalar integer of the maximal order or cumulants required

Value

• the cumulants up to order n of the skew-normal distribution with location=0, scale=1 and shape as selected.

synopsis

sn.cumulants(location = 0, scale = 1, shape = 0, dp = NULL, n = 4)

Details

The moment generating function (hence the cumulant generating function) of the distribution is given in the refence below. The computations method used is proved analytically up to n=3 but it is seen to behave correctly up to the order which was checked (n=8).

References

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.

See Also

dsn,zeta

Examples

sn.cumulants(shape=c(0,2.5,5,10), n=5)
sn.cumulants(dp=c(10,3,-8), n=6)