Confidence Intervals for Common Coefficient of Variation of Several Birnbaum-Saunders Distributions

The Birnbaum-Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). Furthermore, the coefficient of variation (CV) is commonly used to analyze variation within a dataset. In some situations, the independent samples are collected from different instruments or laboratories. Consequently, it is of importance to make inference for the common CV. To this end, confidence intervals based on the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), large-sample (LS), Bayesian credible interval (BayCrI), and highest posterior density interval (HPDI) methods are proposed herein to estimate the common CV of several BS distributions. Their performances in terms of their coverage probabilities and average lengths were investigated by using Monte Carlo simulation. The simulation results indicate that the HPDI-based confidence interval outperformed the others in all of the investigated scenarios. Finally, the efficacies of the proposed confidence intervals are illustrated by applying them to real datasets of PM10 (particulate matter <= 10 mu m) concentrations from three pollution monitoring stations in Chiang Mai, Thailand.

Automated summary

This paper investigates the methods of constructing confidence intervals for estimating the common coefficient of variation (CV) of several Birnbaum-Saunders (BS) distributions. The performances of these methods in terms of coverage probabilities and average lengths are compared. The results show that the HPDI-based confidence interval outperforms the others in all investigated scenarios.