Analysis of Medical Data Using Interval Estimators for Common Mean of Gaussian Distributions with Unknown Coefficients of Variation

Abstract

AbstractThe common mean of Gaussian distributions is a parameter of interest when analyzing medical data. In practice, the population coefficient of variation (CV) is unknown because the population mean and variance are unknown. In this study, the common mean of Gaussian distributions with unknown CVs is considered and four new interval estimators for it using generalized confidence interval (GCI), large sample (LS), adjusted method of variance estimates recovery (adjusted MOVER), and standard bootstrap (SB) approaches are proposed. Furthermore, the proposed interval estimators are compared with a previously reported one based on the GCI approach. Monte Carlo simulation was used to evaluate the performances of the interval estimators based on their coverage probabilities and average lengths, while, medical datasets were used to illustrate the efficacy of these approaches. Our findings show that the interval estimator based on the GCI approach for the common mean of Gaussian distributions with unknown CVs provided the best performance in terms of coverage probability for all sample sizes. However, the adjusted MOVER and SB approaches can be considered as an alternative when the sample size is large (\(n_{i} \ge \) 100).KeywordsAdjusted MOVER approachCVGCI approachMeanSB approach