A Rule-Of-Thumb Method for Obtaining Minimum Variance Estimates of Standard Deviation from Normal Data

摘要

A rule-of-thumb method is derived for reducing a sample of statistically independent data, obtained from an unbiased, circular normal distribution, so as to yield an unbiased, minimum variance estimate of the standard deviation of the parent distribution. By establishment of a mathematical model, the concept of minimum variance is developed, and the rule-of-thumb approximation is derived. Sources of error are considered to determine the accuracy of the method employed. The computational technique employed provides an example of the empirical establishment of a mathematical theorem which is valid over the intended range of its applicability and which cannot, to the author's knowledge, be established in any other manner.