Abstract
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 \({\hat{\theta}_{1}}\) and \({\hat{\theta}_{2}}\) 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.
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Balakrishnan, N., Iliopoulos, G. Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring. Metrika 72, 89–109 (2010). https://doi.org/10.1007/s00184-009-0243-6
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DOI: https://doi.org/10.1007/s00184-009-0243-6