WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Unbiased Estimation of the Standard Deviation for Non-Normal Populations
Author:
Abstract: The bias of the sample standard deviation as an estimator of the population standard deviation, for a simple random sample of size N from a Normal population, is well documented. Exact and approximate bias corrections appear in the literature for this case. However, there has been less discussion of the downward bias of this estimator for non-Normal populations. The appropriate bias correction depends on the kurtosis of the population distribution. We derive and illustrate an approximation for this bias, to $$O(N^{ -1} )$$, for several common distributions.