The Sampling Distribution of Natural Logarithm of Standard Deviation From a Normal Universe
Year: 2025
Type: article
Abstract: 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.
DOI: 10.1002/qre.70095
Authors: Saeed Maghsoodloo, Daniel F. Silva
Institution: Auburn University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4415556808