Standard Errors of Sample Moments

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Description

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

Usage

1
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

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### 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