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)
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. |
Implements the approximate standard error given in Kendall and Stuart (1969), p.243.
The approximate standard error of the sample moment specified.
David Scott d.scott@auckland.ac.nz
Kendall, M. G. and Stuart, A. (1969). The Advanced Theory of Statistics, Volume 1, 3rd Edition. London: Charles Griffin & Company.
### 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
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