On Testing Reduction of Left-Censored Weibull Distribution to Exponential Submodel

Abstract

When analyzing environmental or chemical data, it is often necessary to deal with left-censoredobservations. Since the distribution of the observed variable is often asymmetric, the exponential or the Weibulldistribution can be used. This paper summarizes statistical model of a multiply left-censored Weibull distribution,and estimation of its parameters and their variances using the expected Fisher information matrix. Since inmany situations the Weibull distribution is unnecessarily complicated for data modelling, statistical tests (theLagrange multiplier test, the likelihood ratio test, the Wald test) for assessing suitability of replacement ofthe censored Weibull distribution with the exponential submodel are introduced and their power functions areanalyzed using simulations.