On Testing Reduction of Left-Censored Weibull Distribution to Exponential Submodel
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.
Aboueissa, A.E.-M.A., Stoline, M.R.: Maximum likelihood estimators of population parameters from doubly left-censored samples. Environmetrics 17, 811–826 (2006).
Aboueissa, A.E.-M.A.: Maximum likelihood estimators of population parameters from multiply censored samples. Environmetrics 20, 312–330 (2009)
Antweiler, R.C., Taylor, H.E.: Evaluation of statistical treatments of left-censored environmental data using coincident uncensored data sets: I. Summary statistics. Environmental Science & Technology 42, 3732–3738 (2008)
Antweiler, R.C.: Evaluation of statistical treatments of left-censored environmental data using coincident uncensored data sets: II. Group comparisons. Environmental Science & Technology 49, 13439–13446 (2015)
Cohen, A.C.: Truncated and Censored Samples, Marcel Dekker, New York (1991).
Fusek, M.: Extreme Value Distributions with Applications, doctoral thesis (in Czech), Brno University of Technology, Brno (2013).
Fusek, M., Mich´alek, J.: Statistical methods for analyzing musk compounds concentration based on doubly left-censored samples. International Journal of Mathematical Models and Methods in Applied Sciences 7(8), 755–763 (2013).
Fusek, M., Mich´alek, J.: Statistical analysis of type I multiply left-censored samples from exponential distribution. Journal of Statistical Computation and Simulation 85, 2148–2163 (2015).
Fusek, M., Mich´alek, J., V´avrov´a, M.: Evaluation of contamination data with non-detects using censored distributions. Fresenius Environmental Bulletin 24(11c), 4165–4172 (2015).
Helsel, D.R.: Statistics for Censored Environmental Data using Minitab and R, John Wiley and Sons, New York (2012).
Klein, J.P., Moeschberger, M.L.: Survival Analysis: Techniques for Censored and Truncated Data, second edn. Springer, New York (2005).
Kotb, M.S., Raqab, M.Z.: Inference and prediction for modified Weibull distribution based on doubly censored samples. Mathematics and Computers in Simulation 132, 195–207 (2017).
Krishnamoorthy, K., Mathew, T., Xu, Z.: Comparison of means of two lognormal distributions based on samples with multiple detection limits. Journal of Occupational and Environmental Hygiene 11, 538–546 (2014).
Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM Journal on Optimization 9, 112–147 (1998).
Lehmann, E.L., Casella, G.: Theory of Point Estimation, Springer-Verlag, New York (1998).
Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses, Springer, New York (2005).
Shoari, N., Dub´e, J.-S., Chenouri, S.: Estimating the mean and standard deviation of environmentaldata with below detection limit observations: Considering highly skewed data and model misspecification. Chemosphere 138, 599–608 (2015).
Tekindal, M.A., Erdoˇgan, B.D., Yavuz, Y.: Evaluating left-censored data through substitution, parametric, semi-parametric, and nonparametric methods: A simulation study. Interdisciplinary Sciences: Computational Life Sciences 9, 153–172 (2017).
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