Model Selection Based on Tracking Interval Under Unified Hybrid Censored Samples

The aim of statistical modeling is to identify the model that most closely approximates the underlying process. Akaike information criterion (AIC) is commonly used for model selection but the precise value of AIC has no direct interpretation. In this paper we use a normalization of a difference of Akaike criteria in comparing between the two rival models under unified hybrid censoring scheme. Asymptotic properties of maximum likelihood estimator based on the missing information principle are derived. Also, asymptotic distribution of the normalized difference of AICs is obtained and it is used to construct an interval, say tracking interval, for comparing the two competing models. Monte Carlo simulations are performed to examine how the proposed interval works for different censoring schemes. Two real datasets have been analyzed for illustrative purposes. The first is selecting between Weibull and generalized exponential distributions for main component of spearmint essential oil purification data. The second is the choice between models of the  lifetimes of 20 electronic components.