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

• Main Author: Michal Fusek
• Format: Article
• Language: English
• Published: Brno University of Technology 2017-06-01
• Series: Mendel
• Subjects: Asymptotic tests; multiply left-censored data; Fisher information matrix; maximum likelihood
• Online Access: https://mendel-journal.org/index.php/mendel/article/view/70

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.