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Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring
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Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring
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Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring
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Journal Article
Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring
2010
Overview
In two recent papers by Balakrishnan et al. (J Qual Technol 39:35–47, 2007; Ann Inst Stat Math 61:251–274, 2009), the maximum likelihood estimators
and
of the parameters
θ
1
and
θ
2
have been derived in the framework of exponential simple step-stress models under Type-II and Type-I censoring, respectively. Here, we prove that these estimators are stochastically monotone with respect to
θ
1
and
θ
2
, respectively, which has been conjectured in these papers and then utilized to develop exact conditional inference for the parameters
θ
1
and
θ
2
. For proving these results, we have established a multivariate stochastic ordering of a particular family of trinomial distributions under truncation, which is also of independent interest.
Publisher
Springer-Verlag,Springer Nature B.V
