# 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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*MENDEL*. 23, 1 (Jun. 2017), 179-184. DOI:https://doi.org/10.13164/mendel.2017.1.179.

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