Bayesian Confidence Interval for Ratio of the Coefficients of Variation of Normal Distributions: A Practical Approach in Civil Engineering

The coefficient of variation (CV) is a useful statistical tool for measuring the relative variability between multiple populations, while the ratio of CVs can be used to compare the dispersion. In statistics, the Bayesian approach is fundamentally different from the classical approach. For the Bayesian approach, the parameter is a quantity whose variation is described by a probability distribution. The probability distribution is called the prior distribution, which is based on the experimenter’s belief. The prior distribution is updated with sample information. This updating is done with the use of Bayes’ rule. For the classical approach, the parameter is quantity and an unknown value, but the parameter is fixed. Moreover, the parameter is based on the observed values in the sample. Herein, we develop a Bayesian approach to construct the confidence interval for the ratio of CVs of two normal distributions. Moreover, the efficacy of the Bayesian approach is compared with two existing classical approaches: the generalised confidence interval (GCI) and the method of variance estimates recovery (MOVER) approaches. A Monte Carlo simulation was used to compute the coverage probability (CP) and average length (AL) of three confidence intervals. The results of a simulation study indicate that the Bayesian approach performed better in terms of the CP and AL. Finally, the Bayesian and two classical approaches were applied to analyse real data to illustrate their efficacy. In this study, the application of these approaches for use in classical civil engineering topics is targeted. Two real data, which are used in the present study, are the compressive strength data for the investigated mixes at 7 and 28 days, as well as the PM2.5 air quality data of two stations in Chiang Mai province, Thailand. The Bayesian confidence intervals are better than the other confidence intervals for the ratio of CVs of normal distributions. 

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