boot (version 1.2-13)

cum3: Calculate Third Order Cumulants

Description

Calculates an estimate of the third cumulant, or skewness, of a vector. Also, if more than one vector is specified, a product-moment of order 3 is estimated.

Usage

cum3(a, b=a, c=a, unbiased=TRUE)

Arguments

a

A vector of observations.

b

Another vector of observations, if not supplied it is set to the value of a. If supplied then it must be the same length as a.

c

Another vector of observations, if not supplied it is set to the value of a. If supplied then it must be the same length as a.

unbiased

A logical value indicating whether the unbiased estimator should be used.

Value

• The required estimate.

Details

The unbiased estimator uses a multiplier of n/((n-1)*(n-2)) where n is the sample size, if unbiased is FALSE then a multiplier of 1/n is used. This is multiplied by sum((a-mean(a))*(b-mean(b))*(c-mean(c))) to give the required estimate.