Simulation comparison of modified confidence intervals based on robust estimators for coefficient of variation: skewed distributions case with real applications

Abstract

In this article, we propose confidence intervals for the population coefficient of variation based on some robust estimators such as trimmed mean, winsorized mean, Hodges-Lehmann estimator and trimean. The proposed confidence intervals and their bootstrap versions were compared with the existing confidence intervals for the population coefficient of variation. The performances of the proposed confidence intervals were evaluated via a Monte-Carlo simulation study by considering the coverage probability, average width, standard deviation of widths, and coefficient of variation of widths as comparison criteria. The proposed confidence intervals performed well in terms of coverage probability on symmetrical distributions. In the case of skewed distributions, they were closer to the nominal confidence level and had narrower widths than the others. As a result, we proposed to use confidence intervals based on the Hodges-Lehmann estimator and winsorized mean for small sample sizes ($n=10\text{and}15$) and larger sample sizes for skewed distributions, respectively. The real-life datasets were analyzed to support the simulation results and confirm the practical applications of the proposed confidence intervals.

Keywords:

• Average width
• bootstrap
• coefficient of variation
• coverage probability
• Hodges-Lehmann estimator
• trimean
• trimmed mean
• winsorized mean

Authors’ contributions

All authors contributed equally and significantly in writing of this article. All authors have read and agreed the last version of the paper.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement

The information that assists the conclusions of the present research are included in the paper’s application section.

Additional information

Funding

The authors weren’t financially supported by this research.