Stochastic monotonicity of the
MLEs of parameters in exponential simple step-stress models
under Type-I and Type-II
censoring
N. Balakrishnan and G. Iliopoulos
In
two recent papers by Balakrishnan, Kundu, Ng and Kannan (Journal of Quality
Technology, 2007) and Balakrishnan, Xie and Kundu (Annals of the Institute of
Statistical Mathematics, 2009), the maximum likelihood estimators
$\hat{\theta}_{1}$ and $\hat{\theta}_{2}$ of the parameters $\theta_{1}$ and
$\theta_{2}$ 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 $\theta_{1}$ and $\theta_{2}$,
respectively, which has been conjectured in these papers and then
utilized to develop exact conditional inference for the parameters $\theta_1$
and $\theta_2$. 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.
Key words and phrases: Exponential
distribution; maximum likelihood estimation; step-stress models; Type-II
censoring; Type-I censoring; exact confidence intervals; trinomial
distribution; multivariate stochastic ordering.
Download (207Kb) (The original
publication is available at www.springerlink.com)