Estimating the Population Coefficient of Variation by Confidence Intervals

Abstract

Several researchers considered various interval estimators for estimating the population coefficient of variation (CV) of symmetric and skewed distributions. Since they considered at different times and under different simulation conditions, their performances are not comparable as a whole. In this article, an attempt has been made to review some existing estimators along with some proposed methods and compare them under the same simulation condition. In particular, we have considered Hendricks and Robey, Mckay, Miller, Sharma and Krishna, Curto and Pinto, and also some bootstrap proposed interval estimators for estimating the population CV. A simulation study has been conducted to compare the performance of the estimators. Both average widths and coverage probabilities are considered as a criterion of the good estimators. Two real life health related data sets are analyzed to illustrate the findings of the article. Based on the simulation study, some possible good interval estimators have been recommended for the practitioners.

Keywords:

• Bootstrap methods
• Coefficient of variation
• Confidence interval
• Coverage probability
• Simulation study
• Skewed distributions

Mathematics Subject Classification:

• 62F10
• 62F35

Acknowledgments

The authors are grateful to the Editor and four referees for their excellent and constructive comments/suggestions that greatly improved the presentation and quality of the article. This article was partially completed while the second author was on sabbatical leave (2010–2011). He is grateful to Florida International University for awarding him the sabbatical leave which gave him excellent research facilities.

Notes

Note: n – Sample size; HR – Ordinary t; McK – Makay; MiL – Miller; SK – Sharma and Krishna; CP – Curto and Pinto; NB – Nonparametric Bootstrap; PB – Parametric Bootstrap; BMiL1 – Bootstrap Miller 1; BMiL2 – Bootstrap Miller 2; BCP – Bootstrap Curto and Pinto.

Note: n – Sample size; HR – Ordinary t; McK – Makay; MiL – Miller; SK – Sharma and Krishna; CP – Curto and Pinto; NB – Nonparametric Bootstrap; PB – Parametric Bootstrap; BMiL1 – Bootstrap Miller 1; BMiL2 – Bootstrap Miller 2; BCP – Bootstrap Curto and Pinto.

Note: n – Sample size; HR – Ordinary t; McK – Makay; MiL – Miller; SK – Sharma and Krishna; CP – Curto and Pinto; NB – Nonparametric Bootstrap; PB – Parametric Bootstrap; BMiL1 – Bootstrap Miller 1; BMiL2 – Bootstrap Miller 2; BCP – Bootstrap Curto and Pinto.

Note: n – Sample size; HR – Ordinary t; McK – Makay; MiL – Miller; SK – Sharma and Krishna; CP – Curto and Pinto; NB – Nonparametric Bootstrap; PB – Parametric Bootstrap; BMiL1 – Bootstrap Miller 1; BMiL2 – Bootstrap Miller 2; BCP – Bootstrap Curto and Pinto.

Note: n – Sample size; HR – Ordinary t; McK – Makay; MiL – Miller; SK – Sharma and Krishna; CP – Curto and Pinto; NB – Nonparametric Bootstrap; PB – Parametric Bootstrap; BMiL1 – Bootstrap Miller 1; BMiL2 – Bootstrap Miller 2; BCP – Bootstrap Curto and Pinto.