Use of Lèvy distribution to analyze longitudinal data with asymmetric distribution and presence of left censored data

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 Lèvy 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.

Bayesian Approach for estimating the unknown Scale parameter of Erlang Distribution Based on General Entropy Loss Function

“…The Simulation method was conducted by using MATLAB-R2018a program, under 5000 replications is assumed, we generated different random samples of sizes n = (15,25,50)…”

“…By assuming the standard Levy distribution [15]as prior distribution for unknown scale parameter  when shape parameter η is known with the probability density function (pdf) given by…”

Aplicación de modelos paramétricos alternativos para el análisis de supervivencia de pacientes con cáncer

“…Por el contrario, la metodología podría desarrollarse utilizando otras distribuciones de probabilidad, por ejemplo, se pueden considerar distribuciones capaces de modelar funciones de riesgo con forma de bañera, siendo ésta una función difícil de encontrar dentro los modelos de supervivencia tradicionales (29) . Igualmente, distribuciones con colas pesadas que favorezcan la modelación de conjuntos de datos que presentan valores extremos de importancia, los cuales dependerán del contexto en que se analicen (30) .…”

Volatility clustering in data breach counts

“…A more serious aspect to consider further in the INGARCH model is a model endogeneity, as exemplified by the evidence in the financial sector that volatility of large stocks can be both endogenous or exogenous (Sornette et al, 2004). Achcar et al (2018) used a Lévy distribution in the presence of left censored data and covariates. Third goal of our study is to test a selection of external covariates and their lagged time series for possible drivers of clustering volatility of data breach occurrences.…”