Academic Journal
The Sampling Distribution of Natural Logarithm of Standard Deviation From a Normal Universe.
| Title: | The Sampling Distribution of Natural Logarithm of Standard Deviation From a Normal Universe. |
|---|---|
| Authors: | Maghsoodloo, Saeed1 (AUTHOR) maghsood@eng.auburn.edu, Silva, Daniel F.1 (AUTHOR) |
| Source: | Quality & Reliability Engineering International. Mar2026, Vol. 42 Issue 2, p767-773. 7p. |
| Subject Terms: | *Standard deviations, *Kurtosis, *Statistical sampling, *Logarithms, *Gaussian distribution, *Deviation (Statistics), *Moments method (Statistics) |
| Abstract: | In this article we first derive the sampling distribution of y = loge(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 loge(S). We will determine if there is sample size n beyond which both the skewness and kurtosis of loge(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 loge(S) will also be discussed in a future article. [ABSTRACT FROM AUTHOR] |
| Database: | Academic Search Index |
Be the first to leave a comment!