General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

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.

Evaluating the efficiency of fractional integration parameter estimators

This article deals with the efficiency of fractional integration parameter estimators. This study was based on Monte Carlo experiments involving simulated stochastic processes with integration orders in the range]-1,1[. The evaluated estimation methods were classified into two groups: heuristics and semiparametric/maximum likelihood (ML). The study revealed that the comparative efficiency of the estimators, measured by the lesser mean squared error, depends on the stationary/non-stationary and persistency/anti-persistency conditions of the series. The ML estimator was shown to be superior for stationary persistent processes; the wavelet spectrum-based estimators were better for non-stationary mean reversible and invertible anti-persistent processes; the weighted periodogram-based estimator was shown to be superior for non-invertible anti-persistent processes.

Asymptotically almost periodic solutions for abstract neutral integro-differential equations

We study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations which arise in the study of heat conduction in fading memory material is considered. (C) 2011 Elsevier Inc. All rights reserved.

Expectation Propagation with Factorizing Distributions: A Gaussian Approximation and Performance Results for Simple Models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Scale-free network of a dengue epidemic

In this work we show that the dengue epidemic in the city of Singapore organized itself into a scale-free network of transmission as the 2000-2005 outbreaks progressed. This scale-free network of cluster comprised geographical breeding places for the aedes mosquitoes, acting as super-spreaders nodes in a network of transmission. The geographical organization of the network was analysed by the corresponding distribution of weekly number of new cases. Therefore, our hypothesis is that the distribution of dengue cases reflects the geographical organization of a transmission network, which evolved towards a power law as the epidemic intensity progressed until 2005. (c) 2007 Elsevier Inc. All rights reserved.

An optimization model for antibiotic use

There is a positive correlation between the intensity of use of a given antibiotic and the prevalence of resistant strains. The more you treat, more patients infected with resistant strains appears and, as a consequence, the higher the mortality due to the infection and the longer the hospitalization time. In contrast, the less you treat, the higher the mortality rates and the longer the hospitalization time of patients infected with sensitive strains that could be successfully treated. The hypothesis proposed in this paper is an attempt to solve such a conflict: there must be an optimum treatment intensity that minimizes both the additional mortality and hospitalization time due to the infection by both sensitive and resistant bacteria strains. In order to test this hypothesis we applied a simple mathematical model that allowed us to estimate the optimum proportion of patients to be treated in order to minimize the total number of deaths and hospitalization time due to the infection in a hospital setting. (C) 2007 Elsevier Inc. All rights reserved.

The association of prevalent medial meniscal pathology with cartilage loss in the medial tibiofemoral compartment over a 2-year period

Objective: To investigate the association of different types of magnetic resonance imaging (MRI)-detected medial meniscal pathology with subregional cartilage loss in the medial tibiofemoral compartment. Methods: A total of 152 women aged >= 40 years, with and without knee osteoarthritis (OA) were included in a longitudinal 24-month observational study. Spoiled gradient recalled acquisitions at steady state (SPGR) and T2-weighted fat-suppressed MRI sequences were acquired. Medial meniscal status of the anterior horn (AH), body, and posterior horn (PH) was graded at baseline: 0 (normal), 1 (intrasubstance meniscal signal changes), 2 (single tears), and 3 (complex tears/maceration). Cartilage segmentation was performed at baseline and 24-month follow-up in various tibiofemoral subregions using computation software. Multiple linear regression models were applied for the analysis with cartilage loss as the outcome. In a first model, the results were adjusted for age and body mass index (BMI). In a second model, the results were adjusted for age, BMI and medial meniscal extrusion. Results: After adjusting for age, BMI, and medial meniscal extrusion, cartilage loss in the total medial tibia (MT) (0.04 mm, P=0.04) and the external medial tibia (eMT) (0.068 mm, P=0.04) increased significantly for compartments with grade 3 lesions. Cartilage loss in the total central medial femoral condyle (cMF) (0.071 mm, P=0.03) also increased significantly for compartments with grade 2 lesions. Cartilage loss at the eMT was significantly related to tears of the PH (0.074 mm; P=0.03). Cartilage loss was not significantly increased for compartments with grade 1 lesions. Conclusion: The protective function of the meniscus appears to be preserved in the presence of intrasubstance meniscal signal changes. Prevalent single tears and meniscal maceration were found to be associated with increased cartilage loss in the same compartment, especially at the PH. (C) 2009 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

Survival of Dental Implants in the Cleft Area-A Retrospective Study

Objective To evaluate the survival rate of dental implants placed in the cleft area Design Retrospective study Setting Hospital for Rehabilitation of Craniofacial Anomalies, Brazil Institutional Tertiary Healthcare Center Patients 120 patients who received dental implants in the grafted cleft area in the years 1999 to 2005 Interventions Clinical data were evaluated from the records of 120 patients according to the following criteria placement grafted, cleft area, and age at surgery, age at placement of dental implants, site and dimension of implants, interval between placement of implants and the last clinical follow-up, and interval between placement and removal or indication for removal of implants Main Outcome Measures Percentage of survival rate of implants Results Mean age at placement of the bone graft was 17 6 years and 21 years at placement of implants A total of 123 cleft areas received secondary bone graft and bone graft to install implants (regraft) The mean survival rate was 34 months since placement of the implant to the last clinical follow-up and 26 months since placement of the prosthesis Seven dental implants were removed The survival rate since placement to the last clinical follow-up was 94 3% Conclusion Rehabilitation of the cleft area with dental implants is a viable and secure alternative, with good prognosis