The McDonald inverted beta distribution

We introduce a five-parameter continuous model, called the McDonald inverted beta distribution, to extend the two-parameter inverted beta distribution and provide new four- and three-parameter sub-models. We give a mathematical treatment of the new distribution including expansions for the density function, moments, generating and quantile functions, mean deviations, entropy and reliability. The model parameters are estimated by maximum likelihood and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

General results for the Kumaraswamy-G distribution

For any continuous baseline G distribution [G. M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883-898], proposed a new generalized distribution (denoted here with the prefix 'Kw-G'(Kumaraswamy-G)) with two extra positive parameters. They studied some of its mathematical properties and presented special sub-models. We derive a simple representation for the Kw-Gdensity function as a linear combination of exponentiated-G distributions. Some new distributions are proposed as sub-models of this family, for example, the Kw-Chen [Z.A. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), pp. 155-161], Kw-XTG [M. Xie, Y. Tang, and T.N. Goh, A modified Weibull extension with bathtub failure rate function, Reliab. Eng. System Safety 76 (2002), pp. 279-285] and Kw-Flexible Weibull [M. Bebbington, C. D. Lai, and R. Zitikis, A flexible Weibull extension, Reliab. Eng. System Safety 92 (2007), pp. 719-726]. New properties of the Kw-G distribution are derived which include asymptotes, shapes, moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, reliability, Renyi entropy and Shannon entropy. New properties of the order statistics are investigated. We discuss the estimation of the parameters by maximum likelihood. We provide two applications to real data sets and discuss a bivariate extension of the Kw-G distribution.

Generalized beta-generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets. (c) 2011 Elsevier B.V. All rights reserved.

Height-diameter relationships of tropical Atlantic moist forest trees in southeastern Brazil

Site-specific height-diameter models may be used to improve biomass estimates for forest inventories where only diameter at breast height (DBH) measurements are available. In this study, we fit height-diameter models for vegetation types of a tropical Atlantic forest using field measurements of height across plots along an altitudinal gradient. To fit height-diameter models, we sampled trees by DBH class and measured tree height within 13 one-hectare permanent plots established at four altitude classes. To select the best model we tested the performance of 11 height-diameter models using the Akaike Information Criterion (AIC). The Weibull and Chapman-Richards height-diameter models performed better than other models, and regional site-specific models performed better than the general model. In addition, there is a slight variation of height-diameter relationships across the altitudinal gradient and an extensive difference in the stature between the Atlantic and Amazon forests. The results showed the effect of altitude on tree height estimates and emphasize the need for altitude-specific models that produce more accurate results than a general model that encompasses all altitudes. To improve biomass estimation, the development of regional height-diameter models that estimate tree height using a subset of randomly sampled trees presents an approach to supplement surveys where only diameter has been measured.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

The McDonald extended distribution: properties and applications

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.

Microencapsulation of Ketoprofen in Blends of Acrylic Resins by Spray Drying

Microparticles of ketoprofen entrapped in blends of acrylic resins (Eudragit RL 30D and RS 30D) were successfully produced by spray drying. The effects of the proportion ketoprofen : polymer (1: 1 and 1: 3) and of spray-drying parameters (drying gas inlet temperatures of 80 and 100 degrees C; microencapsulating composition feed flow rates of 4 and 6 g/min) on the microparticles properties (drug content, encapsulation efficiency, mean particle size, moisture content, and dissolution behavior) were evaluated. Differential scanning calorimetry (DSC) thermograms and X-ray diffractograms of the spray-dried product, the free drug, and the physical mixture between the free drug and spray-dried composition (blank) were carried out. Microparticles obtained at inlet temperature of 80 degrees C, feed flow rate of 4 g/min, and ketoprofen : acrylic resin ratio of 1: 3 presented an encapsulation efficiency of 88.1%, moisture content of 5.8%, production yield around 50%, and a higher reduction in dissolution rate of the entrapped ketoprofen. Sigmoidal shape dissolution profiles were presented by the spray-dried microparticles. The dissolution profiles were relatively well described by the Weibull model, a showing high coefficient of determination, R-2, and a mean absolute error between experimental and estimated values of between 4.6 and 10.1%.

Fatigue Reliability of 3 Single-Unit Implant-Abutment Designs

Objectives: Because the mechanical behavior of the implant-abutment system is critical for the longevity of implant-supported reconstructions, this study evaluated the fatigue reliability of different implant-abutment systems used as single-unit crowns and their failure modes. Methods and Materials: Sixty-three Ti-6Al-4V implants were divided in 3 groups: Replace Select (RS); IC-IMP Osseotite; and Unitite were restored with their respective abutments. Anatomically correct central incisor metal crowns were cemented and subjected to separate single load to failure tests and step-stress accelerated life testing (n = 18). A master Weibull curve and reliability for a mission of 50,000 cycles at 200 N were calculated. Polarized-light and scanning electron microscopes were used for failure analyses. Results: The load at failure mean values during step-stress accelerated life testing were 348.14 N for RS, 324.07 N for Osseotite, and 321.29 N for the Unitite systems. No differences in reliability levels were detected between systems, and only the RS system mechanical failures were shown to be accelerated by damage accumulation. Failure modes differed between systems. Conclusions: The 3 evaluated systems did not present significantly different reliability; however, failure modes were different. (Implant Dent 2012;21:67-71)

Tecniche MonteCarlo per l'analisi di sistemi a rete

The assessment of the RAMS (Reliability, Availability, Maintainability and Safety) performances of system generally includes the evaluations of the “Importance” of its components and/or of the basic parameters of the model through the use of the Importance Measures. The analytical equations proposed in this study allow the estimation of the first order Differential Importance Measure on the basis of the Birnbaum measures of components, under the hypothesis of uniform percentage changes of parameters. The aging phenomena are introduced into the model by assuming exponential-linear or Weibull distributions for the failure probabilities. An algorithm based on a combination of MonteCarlo simulation and Cellular Automata is applied in order to evaluate the performance of a networked system, made up of source nodes, user nodes and directed edges subjected to failure and repair. Importance Sampling techniques are used for the estimation of the first and total order Differential Importance Measures through only one simulation of the system “operational life”. All the output variables are computed contemporaneously on the basis of the same sequence of the involved components, event types (failure or repair) and transition times. The failure/repair probabilities are forced to be the same for all components; the transition times are sampled from the unbiased probability distributions or it can be also forced, for instance, by assuring the occurrence of at least a failure within the system operational life. The algorithm allows considering different types of maintenance actions: corrective maintenance that can be performed either immediately upon the component failure or upon finding that the component has failed for hidden failures that are not detected until an inspection; and preventive maintenance, that can be performed upon a fixed interval. It is possible to use a restoration factor to determine the age of the component after a repair or any other maintenance action.

Strategie manutentive e gestione del magazzino, un'applicazione aeronautica

Il presente documento intende illustrare l’applicazione delle moderne teorie dell’affidabilità, delle politiche manutentive e della gestione dei ricambi in ambito aeronautico. Partendo dall’utilizzo di dati forniti da un’azienda operante nel settore è stato elaborato uno studio sperimentale con lo scopo di ricercare la miglior politica manutentiva, con l'obiettivo di minimizzare i costi di manutenzione e di gestione delle scorte a magazzino. La ricerca dell’ottimizzazione dei costi di gestione, senza penalizzare qualità ed efficienza, rappresenta infatti sempre di più un fattore competitivo per le aziende. Lo sviluppo sperimentale si è svolto tramite software specialistici utilizzati nel campo dello studio dell’affidabilità: tramite Weibull++® si sono valutati i parametri delle distribuzioni che descrivono la probabilità di guasto dei singoli componenti e, a partire da questi dati, sono state studiate le possibili politiche manutentive per ciascun componente ed i costi relativi in BlockSim®. Dapprima sono state confrontate diverse strategie manutentive: correttiva pura e preventiva. Alla scelta della miglior politica manutentiva è stata affiancato lo studio delle strategie di gestione del magazzino, al fine di individuare la più efficace. Sia lo studio della manutenzione che quello della gestione del magazzino sono stati affiancati dalla valutazione di impatto economico.

Strength development of single beech wood veneers considering different climate conditions

La tesi di laurea è stata svolta presso l’Università di Scienze Applicate di Rosenheim, in Germania; il progetto di ricerca si basa sulla tecnica di rinforzo conosciuta come “Soil Nailing”, che consiste nella costruzione di un’opera di sostegno nella realizzazione di pareti di scavo o nel consolidamento di versanti instabili. L’obiettivo principale dell’elaborato sarà quello di valutare la fattibilità dell’impiego di tubi fabbricati con legno di faggio, in sostituzione dei chiodi d’acciaio comunemente utilizzati; la scelta di questo tipo di legno è dettata dalla larga disponibilità presente in Germania. La sollecitazione principale su tali tubi sarà di trazione parallela alla fibratura, tramite test sperimentali è stato possibile valutare tale resistenza nelle diverse condizioni in cui si verrà a trovare il tubo dopo l’installazione nel terreno. A tal proposito è necessario specificare che, l’indagine per risalire all’influenza che le condizioni ambientali esercitano sull’elemento, verrà condotta su provini costituiti da un singolo strato di legno; in tal modo si può apprezzare l’influenza direttamente sull’elemento base e poi risalire al comportamento globale. I dati ottenuti dall’indagine sperimentale sono stati elaborati tramite la teoria di Weibull, largamente utilizzata in tecnologia dei materiali per quanto riguarda materiali fragili come il legno; tali distribuzioni hanno permesso la determinazione della resistenza caratteristica dei provini per ogni condizione ambientale d’interesse. Per quanto riguarda la valutazione della fattibilità dell’uso di tubi in legno in questa tecnica di consolidamento, è stato eseguito il dimensionamento del tubo, utilizzando i dati a disposizione ottenuti dall’indagine sperimentale eseguita; ed infine sono state eseguite le verifiche di stabilità dell’intervento.

Investigating interocclusal perception in tactile teeth sensibility using symmetric and asymmetric analysis

The purpose of this clinical trial was to determine the active tactile sensibility of natural teeth and to obtain a statistical analysis method fitting a psychometric function through the observed data points. On 68 complete dentulous test persons (34 males, 34 females, mean age 45.9 ± 16.1 years), one pair of healthy natural teeth each was tested: n = 24 anterior teeth and n = 44 posterior teeth. The computer-assisted, randomized measurement was done by having the subjects bite on thin copper foils of different thickness (5-200 µm) inserted between the teeth. The threshold of active tactile sensibility was defined by the 50% value of correct answers. Additionally, the gradient of the sensibility curve and the support area (90-10% value) as a description of the shape of the sensibility curve were calculated. For modeling the sensibility curve, symmetric and asymmetric functions were used. The mean sensibility threshold was 14.2 ± 12.1 µm. The older the subject, the higher the tactile threshold (r = 0.42, p = 0.0006). The support area was 41.8 ± 43.3 µm. The higher the 50% threshold, the smaller the gradient of the curve and the larger the support area. The curves showing the active tactile sensibility of natural teeth demonstrate a tendency towards asymmetry, so that the active tactile sensibility of natural teeth can mathematically best be described by using the asymmetric Weibull function.

Mortality from road traffic accidents in Switzerland: longitudinal and spatial analyses

Road traffic accidents (RTA) are an important cause of premature death. We examined socio-demographic and geographical determinants of RTA mortality in Switzerland by linking 2000 census data to RTA mortality records 2000-2005 (ICD-10 codes V00-V99). Data from 5.5 million residents aged 18-94 years, 1744 study areas, and 1620 RTA deaths were analyzed, including 978 deaths (60.4%) in motor vehicle occupants, 254 (15.7%) in motorcyclists, 107 (6.6%) in cyclists, and 259 (16.0%) in pedestrians. Weibull survival models and Bayesian methods were used to calculate hazard ratios (HR), and standardized mortality ratios (SMR) across study areas. Adjusted HR comparing women with men ranged from 0.04 (95% CI 0.02-0.07) in motorcyclists to 0.43 (95% CI 0.32-0.56) in pedestrians. There was a u-shaped relationship with age in motor vehicle occupants and motorcyclists. In cyclists and pedestrians, mortality increased after age 55 years. Mortality was higher in individuals with primary education (HR 1.53; 95% CI 1.29-1.81), and higher in single (HR 1.24; 95% CI 1.05-1.46), widowed (HR 1.31; 95% CI 1.05-1.65) and divorced individuals (HR 1.62; 95% CI 1.33-1.97), compared to persons with tertiary education or married persons. The association with education was particularly strong for pedestrians (HR 1.87; 95% CI 1.20-2.91). RTA mortality increased with decreasing population density of study areas for motor vehicle occupants (test for trend p<0.0001) and motorcyclists (p=0.0021) but not for cyclists (p=0.39) or pedestrians (p=0.29). SMR standardized for socio-demographic and geographical variables ranged from 82 to 190. Prevention efforts should aim to reduce inequities across socio-demographic and educational groups, and across geographical areas, with interventions targeted at high-risk groups and areas, and different traffic users, including pedestrians.

Prognosis of patients with HIV-1 infection starting antiretroviral therapy in sub-Saharan Africa: a collaborative analysis of scale-up programmes

Background Prognostic models have been developed for patients infected with HIV-1 who start combination antiretroviral therapy (ART) in high-income countries, but not for patients in sub-Saharan Africa. We developed two prognostic models to estimate the probability of death in patients starting ART in sub-Saharan Africa. Methods We analysed data for adult patients who started ART in four scale-up programmes in Côte d'Ivoire, South Africa, and Malawi from 2004 to 2007. Patients lost to follow-up in the first year were excluded. We used Weibull survival models to construct two prognostic models: one with CD4 cell count, clinical stage, bodyweight, age, and sex (CD4 count model); and one that replaced CD4 cell count with total lymphocyte count and severity of anaemia (total lymphocyte and haemoglobin model), because CD4 cell count is not routinely measured in many African ART programmes. Death from all causes in the first year of ART was the primary outcome. Findings 912 (8·2%) of 11 153 patients died in the first year of ART. 822 patients were lost to follow-up and not included in the main analysis; 10 331 patients were analysed. Mortality was strongly associated with high baseline CD4 cell count (≥200 cells per μL vs <25; adjusted hazard ratio 0·21, 95% CI 0·17–0·27), WHO clinical stage (stages III–IV vs I–II; 3·45, 2·43–4·90), bodyweight (≥60 kg vs <45 kg; 0·23, 0·18–0·30), and anaemia status (none vs severe: 0·27, 0·20–0·36). Other independent risk factors for mortality were low total lymphocyte count, advanced age, and male sex. Probability of death at 1 year ranged from 0·9% (95% CI 0·6–1·4) to 52·5% (43·8–61·7) with the CD4 model, and from 0·9% (0·5–1·4) to 59·6% (48·2–71·4) with the total lymphocyte and haemoglobin model. Both models accurately predict early mortality in patients starting ART in sub-Saharan Africa compared with observed data. Interpretation Prognostic models should be used to counsel patients, plan health services, and predict outcomes for patients with HIV-1 infection in sub-Saharan Africa.

Uncertainty About the Incubation Period of AIDS and its Impact on Backcalculation

We analyze three sets of doubly-censored cohort data on incubation times, estimating incubation distributions using semi-parametric methods and assessing the comparability of the estimates. Weibull models appear to be inappropriate for at least one of the cohorts, and the estimates for the different cohorts are substantially different. We use these estimates as inputs for backcalculation, using a nonparametric method based on maximum penalized likelihood. The different incubations all produce fits to the reported AIDS counts that are as good as the fit from a nonstationary incubation distribution that models treatment effects, but the estimated infection curves are very different. We also develop a method for estimating nonstationarity as part of the backcalculation procedure and find that such estimates also depend very heavily on the assumed incubation distribution. We conclude that incubation distributions are so uncertain that meaningful error bounds are difficult to place on backcalculated estimates and that backcalculation may be too unreliable to be used without being supplemented by other sources of information in HIV prevalence and incidence.