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Approximate two‐sided tolerance intervals for normal mixture distributions
Author(s) -
Tsai ShinFu
Publication year - 2020
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12302
Subject(s) - mathematics , fiducial marker , markov chain monte carlo , markov chain , inference , statistics , population , monte carlo method , algorithm , computer science , artificial intelligence , demography , sociology
Summary Universal 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.