Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.

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.

A search for thermally emitting isolated neutron stars in the 2XMMp catalogue

The relatively large number of nearby radio-quiet and thermally emitting isolated neutron stars (INSs) discovered in the ROSAT All-Sky Survey, dubbed the ""Magnificent Seven"", suggests that they belong to a formerly neglected major component of the overall INS population. So far, attempts to discover similar INSs beyond the solar vicinity failed to confirm any reliable candidate. The good positional accuracy and soft X-ray sensitivity of the EPIC cameras onboard the XMM-Newton satellite allow us to efficiently search for new thermally emitting INSs. We used the 2XMMp catalogue to select sources with no catalogued candidate counterparts and with X-ray spectra similar to those of the Magnificent Seven, but seen at greater distances and thus undergoing higher interstellar absorptions. Identifications in more than 170 astronomical catalogues and visual screening allowed us to select fewer than 30 good INS candidates. In order to rule out alternative identifications, we obtained deep ESO-VLT and SOAR optical imaging for the X-ray brightest candidates. We report here on the optical follow-up results of our search and discuss the possible nature of 8 of our candidates. A high X-ray-to-optical flux ratio together with a stable flux and soft X-ray spectrum make the brightest source of our sample, 2XMM J104608.7-594306, a newly discovered thermally emitting INS. The X-ray source 2XMM J010642.3+005032 has no evident optical counterpart and should be further investigated. The remaining X-ray sources are most probably identified with cataclysmic variables and active galactic nuclei, as inferred from the colours and flux ratios of their likely optical counterparts. Beyond the finding of new thermally emitting INSs, our study aims at constraining the space density of this Galactic population at great distances and at determining whether their apparently high density is a local anomaly or not.

A nonparametric method for the measurement of size diversity with emphasis on data standardization

The most suitable method for estimation of size diversity is investigated. Size diversity is computed on the basis of the Shannon diversity expression adapted for continuous variables, such as size. It takes the form of an integral involving the probability density function (pdf) of the size of the individuals. Different approaches for the estimation of pdf are compared: parametric methods, assuming that data come from a determinate family of pdfs, and nonparametric methods, where pdf is estimated using some kind of local evaluation. Exponential, generalized Pareto, normal, and log-normal distributions have been used to generate simulated samples using estimated parameters from real samples. Nonparametric methods include discrete computation of data histograms based on size intervals and continuous kernel estimation of pdf. Kernel approach gives accurate estimation of size diversity, whilst parametric methods are only useful when the reference distribution have similar shape to the real one. Special attention is given for data standardization. The division of data by the sample geometric mean is proposedas the most suitable standardization method, which shows additional advantages: the same size diversity value is obtained when using original size or log-transformed data, and size measurements with different dimensionality (longitudes, areas, volumes or biomasses) may be immediately compared with the simple addition of ln k where kis the dimensionality (1, 2, or 3, respectively). Thus, the kernel estimation, after data standardization by division of sample geometric mean, arises as the most reliable and generalizable method of size diversity evaluation

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis

Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.

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.

Quality Control in the Healthcare Industry: An Analysis of Surgery Turnover Times

For virtually all hospitals, utilization rates are a critical managerial indicator of efficiency and are determined in part by turnover time. Turnover time is defined as the time elapsed between surgeries, during which the operating room is cleaned and preparedfor the next surgery. Lengthier turnover times result in lower utilization rates, thereby hindering hospitals’ ability to maximize the numbers of patients that can be attended to. In this thesis, we analyze operating room data from a two year period provided byEvangelical Community Hospital in Lewisburg, Pennsylvania, to understand the variability of the turnover process. From the recorded data provided, we derive our best estimation of turnover time. Recognizing the importance of being able to properly modelturnover times in order to improve the accuracy of scheduling, we seek to fit distributions to the set of turnover times. We find that log-normal and log-logistic distributions are well-suited to turnover times, although further research must validate this finding. Wepropose that the choice of distribution depends on the hospital and, as a result, a hospital must choose whether to use the log-normal or the log-logistic distribution. Next, we use statistical tests to identify variables that may potentially influence turnover time. We find that there does not appear to be a correlation between surgerytime and turnover time across doctors. However, there are statistically significant differences between the mean turnover times across doctors. The final component of our research entails analyzing and explaining the benefits of introducing control charts as a quality control mechanism for monitoring turnover times in hospitals. Although widely instituted in other industries, control charts are notwidely adopted in healthcare environments, despite their potential benefits. A major component of our work is the development of control charts to monitor the stability of turnover times. These charts can be easily instituted in hospitals to reduce the variabilityof turnover times. Overall, our analysis uses operations research techniques to analyze turnover times and identify manners for improvement in lowering the mean turnover time and thevariability in turnover times. We provide valuable insight into a component of the surgery process that has received little attention, but can significantly affect utilization rates in hospitals. Most critically, an ability to more accurately predict turnover timesand a better understanding of the sources of variability can result in improved scheduling and heightened hospital staff and patient satisfaction. We hope that our findings can apply to many other hospital settings.

Liquid-liquid extraction in a pilot scale rotating disc contactor

A study of the hydrodynamics and mass transfer characteristics of a liquid-liquid extraction process in a 450 mm diameter, 4.30 m high Rotating Disc Contactor (R.D.C.) has been undertaken. The literature relating to this type of extractor and the relevant phenomena, such as droplet break-up and coalescence, drop mass transfer and axial mixing has been revjewed. Experiments were performed using the system C1airsol-350-acetone-water and the effects of drop size, drop size-distribution and dispersed phase hold-up on the performance of the R.D.C. established. The results obtained for the two-phase system C1airso1-water have been compared with published correlations: since most of these correlations are based on data obtained from laboratory scale R.D.C.'s, a wide divergence was found. The hydrodynamics data from this study have therefore been correlated to predict the drop size and the dispersed phase hold-up and agreement has been obtained with the experimental data to within +8% for the drop size and +9% for the dispersed phase hold-up. The correlations obtained were modified to include terms involving column dimensions and the data have been correlated with the results obtained from this study together with published data; agreement was generally within +17% for drop size and within +14% for the dispersed phase hold-up. The experimental drop size distributions obtained were in excellent agreement with the upper limit log-normal distributions which should therefore be used in preference to other distribution functions. In the calculation of the overall experimental mass transfer coefficient the mean driving force was determined from the concentration profile along the column using Simpson's Rule and a novel method was developed to calculate the overall theoretical mass transfer coefficient Kca1, involving the drop size distribution diagram to determine the volume percentage of stagnant, circulating and oscillating drops in the sample population. Individual mass transfer coefficients were determined for the corresponding droplet state using different single drop mass transfer models. Kca1 was then calculated as the fractional sum of these individual coefficients and their proportions in the drop sample population. Very good agreement was found between the experimental and theoretical overall mass transfer coefficients. Drop sizes under mass transfer conditions were strongly dependant upon the direction of mass transfer. Drop Sizes in the absence of mass transfer were generally larger than those with solute transfer from the continuous to the dispersed phase, but smaller than those with solute transfer in the opposite direction at corresponding phase flowrates and rotor speed. Under similar operating conditions hold-up was also affected by mass transfer; it was higher when solute transfered from the continuous to the dispersed phase and lower when direction was reversed compared with non-mass transfer operation.

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.