Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Use of Lèvy distribution to analyze longitudinal data with asymmetric distribution and presence of left censored data

  • Achcar, Jorge A. (Departamento de Medicina Social, Universidade de Sao Paulo) ;
  • Coelho-Barros, Emilio A. (Departamento de Matematica, Universidade Federal do Parana) ;
  • Cuevas, Jose Rafael Tovar (Escuela de Estadistica, Universidad del Valle) ;
  • Mazucheli, Josmar (Departamento de Estatistica, Universidade Estadual de Maringa)
  • Received : 2017.07.06
  • Accepted : 2017.12.12
  • Published : 2018.01.31
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Abstract

This paper considers the use of classical and Bayesian inference methods to analyze data generated by variables whose natural behavior can be modeled using asymmetric distributions in the presence of left censoring. Our approach used a $L{\grave{e}}vy$ distribution in the presence of left censored data and covariates. This distribution could be a good alternative to model data with asymmetric behavior in many applications as lifetime data for instance, especially in engineering applications and health research, when some observations are large in comparison to other ones and standard distributions commonly used to model asymmetry data like the exponential, Weibull or log-logistic are not appropriate to be fitted by the data. Inferences for the parameters of the proposed model under a classical inference approach are obtained using a maximum likelihood estimators (MLEs) approach and usual asymptotical normality for MLEs based on the Fisher information measure. Under a Bayesian approach, the posterior summaries of interest are obtained using standard Markov chain Monte Carlo simulation methods and available software like SAS. A numerical illustration is presented considering data of thyroglobulin levels present in a group of individuals with differentiated cancer of thyroid.

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