b4d4897c-f8bf-4a43-9cab-a07dca3608d520220323122119115wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40511520221520222110.37394/23206.2022.21https://wseas.com/journals/mathematics/2022.phpDavid E.GilesDepartment of Economics University of Victoria, Victoria, B.C. CANADAThe 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.3232022323202211912118https://wseas.com/journals/mathematics/2022/a365106-005(2022).pdf10.37394/23206.2022.21.18https://wseas.com/journals/mathematics/2022/a365106-005(2022).pdf10.2307/2681802Bolch, B.W., More on Unbiased Estimation of the Standard Deviation, The American Statistician, 22 (3), 1968, 27. 10.2307/2681734Brugger, R.M., A Note on Unbiased Estimation of the Standard Deviation, The American Statistician, 23 (4), 1969, 32. 10.2307/2681876Cureton, E.E., Unbiased Estimation of the Standard Deviation, The American Statistician, 22 (1), 1968, 22. 10.2307/2682419D’Agostino, R.B., Linear Estimation of the Normal Distribution Standard Deviation, The American Statistician, 24 (3), 1970, 14–15. 10.2307/2682923Gurland, J. and Tripathi, R.C., A Simple Approximation for Unbiased Estimation of the Standard Deviation, The American Statistician, 25 (4), 1971, 30-32. 10.2307/2681801Markowitz, E., Minimum Mean-Square- Error Estimation of the Standard Deviation of the Normal Distribution, The American Statistician, 22 (3), 1968, 26. 10.2307/2681731Stuart, A., Reduced Mean-Square-Error Estimation of 𝜎 𝑝 in Normal Samples, The American Statistician, 23 (4), 1969, 27. Angelova, J.A., On Moments of Sample Mean and Variance, International Journal of Pure and Applied Mathematics, 79 (1), 2012, 67-85. Jarrett, R.F., A Minor Exercise in History,” The American Statistician, 22 (3), 1968, 25. 10.2307/1418879Holtzman, W.H., The Unbiased Estimate of the Population Variance and Standard Deviation,” American Journal of Psychology, 63 (4), 1950, 615-617. 10.1080/00401706.1979.10489785Johnson, M.E. and Lowe Jr., V.W., “Bounds on the Sample Skewness and Kurtosis,” Technometrics, 21 (3), 1979, 377- 378.