One-sided tolerance interval in a two-way balanced nested model with mixed effects
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Publication date
1 April 2013
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Abstract
In many research areas (such as public health, environmental contamination, and
others) one deals with the necessity of using data to infer whether some proportion
(%) of a population of interest is (or one wants it to be) below and/or over some
threshold, through the computation of tolerance interval. The idea is, once a threshold
is given, one computes the tolerance interval or limit (which might be one or
two - sided bounded) and then to check if it satisfies the given threshold.
Since in this work we deal with the computation of one - sided tolerance interval,
for the two-sided case we recomend, for instance, Krishnamoorthy and Mathew [5].
Krishnamoorthy and Mathew [4] performed the computation of upper tolerance
limit in balanced and unbalanced one-way random effects models, whereas Fonseca et al [3] performed it based in a similar ideas but in a tow-way nested mixed or
random effects model. In case of random effects model, Fonseca et al [3] performed
the computation of such interval only for the balanced data, whereas in the mixed
effects case they dit it only for the unbalanced data. For the computation of twosided
tolerance interval in models with mixed and/or random effects we recomend,
for instance, Sharma and Mathew [7].
The purpose of this paper is the computation of upper and lower tolerance interval
in a two-way nested mixed effects models in balanced data. For the case
of unbalanced data, as mentioned above, Fonseca et al [3] have already computed
upper tolerance interval. Hence, using the notions persented in Fonseca et al [3]
and Krishnamoorthy and Mathew [4], we present some results on the construction
of one-sided tolerance interval for the balanced case. Thus, in order to do so at first
instance we perform the construction for the upper case, and then the construction
for the lower case