A Comparison of MLE for Some Index Distributions Based on Censored Samples

This paper elucidates the prerequisites for maximum likelihood estimation (MLE) of parameters within the exponential and scale parameter families. Estimation of these parameters is predicated on data derived from censored samples and seeks to adhere to stochastic ordering principles. The study establishes that for two independent normal distributions and a two-parameter exponential distribution discernible by the distinct parameter sets, the MLEs of the parameters evince a stochastically ordered relationship when evaluated using full datasets. Furthermore, this research is extended to corroborate the persistence of stochastic ordering in the MLEs of such parameters under conditions of fixed censoring of samples.