Approximate two‐sided tolerance intervals for normal mixture distributions

Abstract

SummaryUniversal and individual two‐sided tolerance intervals that take the inherent structure of normal mixture distributions into account are introduced in this paper for the purpose of monitoring the overall population and specific subpopulations. On the basis of generalised fiducial inference, a Markov chain Monte Carlo sampler is proposed to generate realisations from the generalised fiducial distributions of unknown parameters for obtaining the required tolerance intervals. Based on the simulation results, it is shown that the proposed method can maintain the empirical coverage rates sufficiently close to the nominal level. In addition, a lake acidity monitoring study is used to illustrate the proposed method.