momSE function

Standard Errors of Sample Moments

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

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.

Returns

The approximate standard error of the sample moment specified.

References

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

Author(s)

David Scott d.scott@auckland.ac.nz

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