Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

Random walks can undergo transitions from normal diffusion to anomalous diffusion as some relevant parameter varies, for instance the L,vy index in L,vy flights. Here we derive the Fokker-Planck equation for a two-parameter family of non-Markovian random walks with amnestically induced persistence. We investigate two distinct transitions: one order parameter quantifies log-periodicity and discrete scale invariance in the first moment of the propagator, whereas the second order parameter, known as the Hurst exponent, describes the growth of the second moment. We report numerical and analytical results for six critical exponents, which together completely characterize the properties of the transitions. We find that the critical exponents related to the diffusion-superdiffusion transition are identical in the positive feedback and negative feedback branches of the critical line, even though the former leads to classical superdiffusion whereas the latter gives rise to log-periodic superdiffusion.

Listening to the Whispers of Matter Through Arabic Hermeticism: New Studies on the Book of the Treasure of Alexander

The Jabirian Corpus refers to the K. Thahirat Al-`Iskandar, ""The Book of the Treasure of Alexander"" (hereafter BTA), as one of several forgeries suggesting that alchemical secrets were hidden in inscriptions in various places. The book was neglected until 1926, when Julius Ruska discussed it in his work on the Emerald Tablet, placing the BTA within the literature related to the development of Arabic alchemy. His preliminary study became an essential reference and encouraged many scholars to work on the BTA in the following decades. Some years ago, we completed the first translation of the BTA into a Western language. The work was based on the acephalous Escorial manuscript, which we identified as a fourteenth-century copy of the BTA. This manuscript is peculiar, as part of it is encoded. After finishing our translation, we started to establish the text of the BTA. At present, the text is in process of fixation-to be followed by textual criticism-and has been the main focus of a thorough study of ours on medieval hermeticism and alchemy. A sample of the work currently in progress is presented in this paper: an analysis of the variations between different manuscripts along with a study and English translation of its alchemical chapter.

Book illustration, as (intersemiotic) translation: Pictures translating words

This article examines book illustrations through the prism of Translation Studies. It mainly suggests that the pictures in illustrated books are (intersemiotic) translations of the text and that, as such, they can be analyzed making use of the same tools applied to verbal interlingual translation. The first section deals with the theoretical bases upon which illustrations can be regarded as translations, concentrating on theories of re-creation, as illustration is viewed essentially as the re-creation of the text in visual form. One of the claims in this section is that, because illustration is carried out in very similar ways as interlingual translation itself, the term ""intersemiotic"" relates more to the (obvious) difference of medium. For this reason the word is most often referred to in parentheses. The second section discusses three particular ways through which illustrations can translate the text, namely, by reproducing the textual elements literally in the picture, by emphasizing a specific narrative element, and by adapting the pictures to a certain ideology or artistic trend. The example illustrations are extracted from different. kinds of publication and media, ranging from Virgil`s Aeneid, Lewis Carroll`s Alice in Wonderland and Mark Twain`s Adventures of Huckleberry Finn to an online comic version of Shakespeare`s Hamlet.