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-censored
observations. Since the distribution of the observed variable is often asymmetric, the exponential or the Weibull
distribution 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 in
many situations the Weibull distribution is unnecessarily complicated for data modelling, statistical tests (the
Lagrange multiplier test, the likelihood ratio test, the Wald test) for assessing suitability of replacement of
the censored Weibull distribution with the exponential submodel are introduced and their power functions are
analyzed using simulations.
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