The Sampling Distribution of Natural Logarithm of Standard Deviation From a Normal Universe

ABSTRACT In this article we first derive the sampling distribution of y = log e ( S ) where the variate S represents the standard deviation of a sample of size n ≥ 2 from an underlying normal universe. We then use the density of y = Ln( S ) to tabulate the first four moments of log e ( S ). We will determine if there is sample size n beyond which both the skewness and kurtosis of log e ( S ) are within 0.20 of normal zero so that the corresponding normal approximation may be adequate. The quantiles of y will be obtained in a sequel article, and they will be used to assess the normal approximation; the quality control aspects of log e ( S ) will also be discussed in a future article.