# cum3: Calculate Third Order Cumulants In boot: Bootstrap Functions (Originally by Angelo Canty for S)

## 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

 `1` ```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.

## 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.

## Value

The required estimate.

boot documentation built on May 3, 2021, 5:09 p.m.