A Monte Carlo simulation study of two-sided tolerance intervals in balanced one-way random effects model for non-normal errors

Abstract

Recently, Ong and Mukerjee [Probability matching priors for two-sided tolerance intervals in balanced one-way and two-way nested random effects models. Statistics. 2011;45:403–411] developed two-sided Bayesian tolerance intervals, with approximate frequentist validity, for a future observation in balanced one-way and two-way nested random effects models. These were obtained using probability matching priors (PMP). On the other hand, Krishnamoorthy and Lian [Closed-form approximate tolerance intervals for some general linear models and comparison studies. J Stat Comput Simul. 2012;82:547–563] studied closed-form approximate tolerance intervals by the modified large-sample (MLS) approach. We compare the performances of these two approaches for normal as well as non-normal error distributions. Monte Carlo simulation methods are used to evaluate the resulting tolerance intervals with regard to achieved confidence levels and expected widths. It turns out that PMP tolerance intervals are less conservative for data with large number of classes and small number of observations per class and the MLS procedure is preferable for smaller sample sizes.

Keywords:

• Bayesian
• probability matching priors
• frequentist validity
• modified large sample
• t-distribution
• skew-normal
• generalized lambda

2010 Mathematics Subjects Classification:

• 62F15
• 62F25
• 65C05

Acknowledgements

We thank the referees for providing very constructive suggestions which greatly improved the paper. The work was supported by the Fundamental Research Grant FRGS/1-2010/FP003/2010A.