An R implementation for generalized Birnbaum-Saunders distributions

The Birnbaum-Saunders (BS) model is a positively skewed statistical distribution that has received great attention in recent decades. A generalized version of this model was derived based on symmetrical distributions in the real line named the generalized BS (GBS) distribution. The R package named gbs was developed to analyze data from GBS models. This package contains probabilistic and reliability indicators and random number generators from GBS distributions. Parameter estimates for censored and uncensored data can also be obtained by means of likelihood methods from the gbs package. Goodness-of-fit and diagnostic methods were also implemented in this package in order to check the suitability of the GBS models. in this article, the capabilities and features of the gbs package are illustrated by using simulated and real data sets. Shape and reliability analyses for GBS models are presented. A simulation study for evaluating the quality and sensitivity of the estimation method developed in the package is provided and discussed. (C) 2008 Elsevier B.V. All rights reserved.

A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

The Conway-Maxwell-Poisson-generalized gamma regression model with long-term survivors

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

A log-Birnbaum-Saunders regression model with asymmetric errors

This paper introduces a skewed log-Birnbaum-Saunders regression model based on the skewed sinh-normal distribution proposed by Leiva et al. [A skewed sinh-normal distribution and its properties and application to air pollution, Comm. Statist. Theory Methods 39 (2010), pp. 426-443]. Some influence methods, such as the local influence and generalized leverage, are presented. Additionally, we derived the normal curvatures of local influence under some perturbation schemes. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model.

The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

COMPARISON MEASURES OF MAPS GENERATED BY GEOSTATISTICAL METHODS

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

Comparison measures of maps generated by geostatistical methods

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

Populationsgenetik eisenzeitlicher Reiternomaden der Eurasischen Steppe

Vorliegende Dissertation beschäftigt sich mit der Populationsgenetik eisenzeitlicher Bevölkerungen der Eurasischen Steppe, die mit der skythischen Kultur assoziiert werden. Für die Analysen wurden 30 Fragmente der kodierenden Region und die HVR1 (16040–16400) des mitochondrialen Genoms, sowie 20 phänotypische Marker untersucht. Die Marker wurden durch Multiplex-PCRs angereichert, mit einem probenspezifischen barcode versehen und einer parallelen Sequenzanalyse mit dem 454 GS FLX Sequenzierer unterzogen. 97 Individuen wurden erfolgreich analysiert, von denen 19 aus dem Westen der Eurasischen Steppe und 78 aus dem Bereich des Altai-Gebirges stammen. Die populationsgenetischen Analysen ergaben geringe genetische Distanzen zwischen den skythischen Populationen aus dem Bereich des Altai-Gebirges, die sich vom 9. bis zum 3. Jahrhundert vor Christus erstrecken, was für eine kontinuierliche Bevölkerungsentwicklung sprechen könnte. Weiterhin finden sich geringe genetische Distanzen zwischen den Gruppen im Osten und Westen der Eurasischen Steppe, was auf eine gemeinsame Ursprungspopulation, oder zumindest Genfluss hinweisen kann. Die Ergebnisse aus dem Vergleich mit neolithischen und bronzezeitlichen Referenzpopulationen aus Zentralasien und den angrenzenden Gebieten weisen auf die Möglichkeit eines gemeinsamen zentral-asiatischen Ursprungs hin, zeigen aber auch, dass die östlichen und westlichen Gruppen der Eisenzeit jeweils zusätzlich lokalem Genfluss ausgesetzt waren. Die Allelfrequenzen der phänotypischen Marker deuten auf einen größeren europäischen Einfluss auf das östliche Zentralasien in der Eisenzeit hin, oder ansteigenden Genfluss aus Ostasien nach der Eisenzeit.

Pollen and macroremains from profiles from site Osterholz and Elm

The biostratigraphic classification of the Pleistocene in north-western and central Europe is still insufficiently known, in spite of numerous geological and vegetation-history investigations. The question is not even clear, for example, how often a warm-period vegetation with thermophilous trees such as Quercus, Ulmus, Tilia, Carpinus etc could develop here. In past years, on the basis of several geological and vegetation-history findings, suspicion has often been expressed that some of the classical stages of the Pleistocene could include more warm periods than heretofore assumed, and as a result of recent investigations the period between the Waal and Holstein interglacials seems to include at least two warm periods, of which the Cromer is one. This paper contributes to this problem. The interglacial sediments coming from the Elm-Mountains near Brunswick and from the Osterholz near Elze - both within the limits of the German Mittelgebirge - were investigated by pollen analysis. In both cases a Pinus-Betula zone and a QM zone were found. The vegetation development of the Pinus-Betula zone is characterized in both sequences by the early appearance of Picea. Because of strong local influence at the Osterholz a detailed correlation is difficult. However, vegetation development at the time of the QM zone at both sites was similar; it is especially characterized by the facts that Ulmus clearly migrated to the site earlier than Quercus and was very abundant throughout this time. Furthermore, both diagrams show very low amounts of Corylus. The interglacial of the Osterholz shows in addition to the above; a Carpinus-QM-Picea-zone in which Eucommia reaches a relative high value and in the upper of which Azolla filiculoides was also found. The similarity of vegetation development justifies acceptance of the same age for the occurrences. A comparison of the vegetation development at the Elm and the Osterholz with those of the Eem, Holstein, Waal, and Tegelen warm periods as well as with all the Cromer sites so far investigated shows that only a correlation with the Cromer Complex is possible. This correlation is supported by the geologic relations in the Osterholz (the deposit is overlain by Elster till). Therefore the till-like material with Scandinavian rock fragments underlying the deposit at Elm is of particular interest. The 'Rhume' interglacial beds at Bilshausen, only 60 km south of Osterholz, is also assigned to the Cromer complex, but the two deposits cannot be of the same age because the vegetation development differs. Therefore the Cromer complex must include at least two warm periods. Further conclusions about the relative stratigraphic position of these two occurrences and correlations of other Cromer sites are at this time not possible, however.

A nova família de distribuições odd log-logística: teoria e aplicações

Neste trabalho, foi proposta uma nova família de distribuições, a qual permite modelar dados de sobrevivência quando a função de risco tem formas unimodal e U (banheira). Ainda, foram consideradas as modificações das distribuições Weibull, Fréchet, half-normal generalizada, log-logística e lognormal. Tomando dados não-censurados e censurados, considerou-se os estimadores de máxima verossimilhança para o modelo proposto, a fim de verificar a flexibilidade da nova família. Além disso, um modelo de regressão locação-escala foi utilizado para verificar a influência de covariáveis nos tempos de sobrevida. Adicionalmente, conduziu-se uma análise de resíduos baseada nos resíduos deviance modificada. Estudos de simulação, utilizando-se de diferentes atribuições dos parâmetros, porcentagens de censura e tamanhos amostrais, foram conduzidos com o objetivo de verificar a distribuição empírica dos resíduos tipo martingale e deviance modificada. Para detectar observações influentes, foram utilizadas medidas de influência local, que são medidas de diagnóstico baseadas em pequenas perturbações nos dados ou no modelo proposto. Podem ocorrer situações em que a suposição de independência entre os tempos de falha e censura não seja válida. Assim, outro objetivo desse trabalho é considerar o mecanismo de censura informativa, baseado na verossimilhança marginal, considerando a distribuição log-odd log-logística Weibull na modelagem. Por fim, as metodologias descritas são aplicadas a conjuntos de dados reais.

(Table 3, page 280) Chemical composition of micronodules from a series of stations and sediment depths from Areas C, F, G and K in the Pacific Ocean from R/V Sonne Cruise SO06

Compositional data for coexisting manganese nodules, micronodules, sediments and pore waters from five areas in the equatorial and S.W. Pacific have been obtained. This represents the largest study of its type ever undertaken to establish the distribution of elements between the various phases within the sediment column. The composition of manganese nodules, micronodules and sediments (on a carbonate-free basis) shows marked differences between the equatorial high productivity zone and the low productivity region of the S.W. Pacific. In the case of the nodules, th is reflects an increased supply of transition elements (notably Ni, Cu and Zn) to the nodules as a result of the in situ dissolution of siliceous tests within the sediment column in the equatorial Pacific high productivity zone. Micronodules display similar, but somewhat different, compositions to those of the associated nodules in each area. Micronodule composition is therefore influenced by the same basic factors that control nodule composition, but is modified by dissolution of the micronodules in situ within the sediment column. Locally, as in the area immediately south of the Marquesas Fracture Zone, the micronodule population is contaminated by small, angular volcanic rock fragments; this leads to apparently anomalous micronodule compositions. Micronodules appear to be a transient feature in the sediment column, especially in the equatorial Pacific. Dissolution of micronodules in the sediment column therefore represents an important source of elements for the growth of manganese nodules in the equatorial Pacific. Sediment composition is markedly influenced by the carbonate content. On a carbonate-free basis, the sediments from the equatorial high productivity zone are quite distinct in composition from those in the S.W. Pacific. This reflects differences in the lithology of the sediments. In the Aitutaki Passage, the local influence of volcanoclastic material in sediment composition has been established. The major cations and anions in pore waters measured here show no major differences between equatorial and S.W. Pacific sediments. Silica is, however, higher in equatorial Pacific pore waters reflecting the dissolution of siliceous tests in these sediments.