Likelihood-based methods for testing the equality of means of several log-normal populations

Cakmak, Mehmet; Gökpınar, Fikri; Ebegil, Meral; Gökpınar, Esra

doi:10.47974/JSMS-1405

Open Access Research Article

Likelihood-based methods for testing the equality of means of several log-normal populations

Mehmet CakmakStat.mehmetcakmak@gmail.comDepartment of StatisticsGazi UniversityAnkara, 06500, Turkey0000-0001-6036-8956View full profile → , Fikri Gökpınarfikri@gazi.edu.trDepartment of StatisticsGazi UniversityAnkara, 06500, Turkey0000-0002-6310-8727View full profile → , Meral Ebegilmdemirel@gazi.edu.trDepartment of StatisticsGazi UniversityAnkara, 06500, Turkey0000-0003-4798-3422View full profile → , ^*Esra GökpınarCorresponding authoreyigit@gazi.edu.trDepartment of StatisticsGazi UniversityAnkara, 06500, Turkey0000-0003-2148-4940View full profile →

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pp. 559–577Vol. 28Issue 3April 2025DOI: 10.47974/JSMS-1405XML

Received:: 09 Apr 2024
Published Online:: 01 Mar 2025
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1405
Pages:: 559–577

Abstract

In this study, to test the equality of means of several log-normal distributions, our aim is to investigate the effectiveness of likelihood-based methods, such as the likelihood ratio test, the Score test, and the Wald test. For this reason, we propose a Wald test based on the likelihood method. Additionally, the chi-square approximation of the Wald test statistic is often inadequate in small sample scenarios for various problems. To address this, we employ a computational approach test (CAT), known as a type of parametric bootstrap method. To assess the performance of these proposed tests, we evaluate them via their sizes and power under different numbers of groups, sample sizes, and scale parameters. Our simulation study reveals that the CAT of Wald test performs better than the others when the sample sizes and scale parameters within each group are directly proportional. We also provide a data example to illustrate the above methods.

Keywords

Log-normal distribution Likelihood-based methods Parametric bootstrap Heteroscedasticity Simulation

Subject Classifications

62F0362F4065C05

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