sample.centralmoments {sn}R Documentation

Sample centralmoments

Description

Computes sample central moments up to a given order and the first moment from the origin

Usage

sample.centralmoments(x, w = rep(1, length(x)), order=4)

Arguments

x a vector of sample values
w an optional vector of weights
order the maximal order of the central moments to be computed; it must be a positive integer (default value 4)

Details

NA's are allowed but removed. Averaging of appropriate quantities is actually performed by weighted.mean

Value

A vector containing the first sample central moments, in position [2:order], and the first moment from the origin, in the first position of the returned vector

Note

The second component of the returned vector (if order>1) gives the sample variance; notice that it differs from the value returned by var(x), since this gives the corrected sample variance.

Used in conjunction with st.cumulants.inversion, this function allows to fit a skew-t distribution by the methods of moments; see the example below. Note however, that for stability reasons, this is not adopted as the standard method for producing initial values of MLE search.

Author(s)

Adelchi Azzalini

See Also

st.cumulants.inversion, weighted.mean

Examples

data(ais, package='sn')
mom <- sample.centralmoments(ais[,"bmi"])
st.cumulants.inversion(cum=c(mom[1:3], mom[4]-3*mom[2]^2))
# parameters of the fitted ST distribution

[Package sn version 0.4-10 Index]