Small Sample Inference for the Common Coefficient of Variation

TL;DR

This paper introduces a modified signed log-likelihood ratio method for inference on the common coefficient of variation across multiple normal populations, demonstrating improved accuracy and efficiency especially with small samples.

Contribution

It proposes a novel inference method that outperforms existing approaches in terms of coverage probability and interval length for small sample sizes.

Findings

Coverage probability close to the confidence level

Smaller expected length than competing methods

Effective for small sample sizes and multiple populations

Abstract

This paper utilizes the modified signed log-likelihood ratio method for the problem of inference about the common coefficient of variation in several independent normal populations. This method is applicable for both the problem of hypothesis testing and constructing a confidence interval for this parameter. Simulation studies show that the coverage probability of this proposed approach is close to the confidence coefficient. Also, its expected length is smaller than expected lengths of other competing approaches. In fact, the proposed approach is very satisfactory regardless of the number of populations and the different values of the common coefficient of variation even for very small sample size. Finally, we illustrate the proposed method using two real data sets.