R: Standard Errors of Sample Moments

momSE {DistributionUtils} | R Documentation

## Standard Errors of Sample Moments

### Description

Calculates the approximate standard error of the sample variance, sample central third moment and sample central fourth moment.

### Usage

    momSE(order = 4, n, mom)

### Arguments

`order` | Integer: either 2, 3, or 4.
`n` | Integer: the sample size.
`mom` | Numeric: The central moments of order 1 to 2n of the distribution being sampled from.

### Details

Implements the approximate standard error given in Kendall and Stuart (1969), p.243.

### Value

The approximate standard error of the sample moment specified.

### Author(s)

David Scott d.scott@auckland.ac.nz

### References

Kendall, M. G. and Stuart, A. (1969). The Advanced Theory of Statistics, Volume 1, 3rd Edition. London: Charles Griffin & Company.

### See Also

`momChangeAbout`

### Examples

    ### Moments of the normal distribution, mean 1, variance 4
    mu <- 1
    sigma <- 2
    mom <- c(0,sigma^2,0,3*sigma^4,0,15*sigma^6,0,105*sigma^8)
    ### standard error of sample variance
    momSE(2, 100, mom[1:4])
    ### should be
    sqrt(2*sigma^4)/10
    ### standard error of sample central third moment
    momSE(3, 100, mom[1:6])
    ### should be
    sqrt(6*sigma^6)/10
    ### standard error of sample central fourth moment
    momSE(4, 100, mom)
    ### should be
    sqrt(96*sigma^8)/10

[Package DistributionUtils version 0.6-0 Index]