Stochastic monotonicity of the MLE of exponential mean
under different censoring schemes
N. Balakrishnan and G. Iliopoulos
In this paper, we present a general
method which can be used in order to show that the maximum likelihood estimator
(MLE) of an exponential mean $\theta$ is stochastically increasing with respect
to $\theta$ under different censored sampling schemes. This propery is
essential for the construction of exact confidence intervals for $\theta$ via
``pivoting the cdf'' as well as for the tests of hypotheses about $\theta$. The
method is shown for Type-I censoring, hybrid censoring and generalized hybrid
censoring schemes. We also establish the
result for the exponential competing risks model with censoring.
Key words and phrases: Exponential
distribution, maximum likelihood estimation, Type-I censoring, Type-I and
Type-II hybrid censoring, Type-I and Type-II generalized hybrid censoring,
exact confidence intervals, stochastic ordering, competing risks model.
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