Confidence estimation of the ratio of variances of two log-normal populations

This study investigates asymptotic and bootstrap confidence intervals (CIs) for the ratio of variances of two independent log-normal distributions. Extensive simula-tions were conducted to evaluate the performance of these CIs under varying sample sizes (10 to 350) and variance ratios, with one variance fixed at 0.1 and the other varying from 0.1 to 2.0. The impacts of equal and unequal were studied. The results reveal that the asymptotic CI performs well for small variance differences, especially with moderate to large sample sizes, while bootstrap CIs outperform it for larger variance differences. Notably, the t-bootstrap CI excels when both the variance dif-ference and sample sizes are large, whereas the percentile and standard bootstrap CIs are preferable for small variance differences. The study also demonstrates the practical application of these methods using PM2.5 mass concentration data from two industrial sites in Thailand, confirming their effectiveness in real-world scenarios. Keywords: Log-normal distribution, Ratio of variances, Asymptotic confidence inter-val, Bootstrap confidence interval.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2025

Author dc:creator

• Tantikhajorngosol, Puttipong

Advisor dc:contributor.advisor

• Volodin, Andrei

Committee member dc:contributor.committeemember

• Sardarli, Arzu

Language dc:language.iso

en

DOI

https://doi.org/10.82465/161

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/17141