cum3 {boot} R Documentation

## 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.

### 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.

[Package boot version 1.2-27 Index]