The Kumaraswamy Weibull distribution with application to failure data

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

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.

Leaf area index estimation with MODIS reflectance time series and model inversion during full rotations of Eucalyptus plantations

The leaf area index (LAI) of fast-growing Eucalyptus plantations is highly dynamic both seasonally and interannually, and is spatially variable depending on pedo-climatic conditions. LAI is very important in determining the carbon and water balance of a stand, but is difficult to measure during a complete stand rotation and at large scales. Remote-sensing methods allowing the retrieval of LAI time series with accuracy and precision are therefore necessary. Here, we tested two methods for LAI estimation from MODIS 250m resolution red and near-infrared (NIR) reflectance time series. The first method involved the inversion of a coupled model of leaf reflectance and transmittance (PROSPECT4), soil reflectance (SOILSPECT) and canopy radiative transfer (4SAIL2). Model parameters other than the LAI were either fixed to measured constant values, or allowed to vary seasonally and/or with stand age according to trends observed in field measurements. The LAI was assumed to vary throughout the rotation following a series of alternately increasing and decreasing sigmoid curves. The parameters of each sigmoid curve that allowed the best fit of simulated canopy reflectance to MODIS red and NIR reflectance data were obtained by minimization techniques. The second method was based on a linear relationship between the LAI and values of the GEneralized Soil Adjusted Vegetation Index (GESAVI), which was calibrated using destructive LAI measurements made at two seasons, on Eucalyptus stands of different ages and productivity levels. The ability of each approach to reproduce field-measured LAI values was assessed, and uncertainty on results and parameter sensitivities were examined. Both methods offered a good fit between measured and estimated LAI (R(2) = 0.80 and R(2) = 0.62 for model inversion and GESAVI-based methods, respectively), but the GESAVI-based method overestimated the LAI at young ages. (C) 2010 Elsevier Inc. All rights reserved.

Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Accelerating seismic energy release and evolution of event time and size statistics: Results from two heterogeneous cellular automaton models

The evolution of event time and size statistics in two heterogeneous cellular automaton models of earthquake behavior are studied and compared to the evolution of these quantities during observed periods of accelerating seismic energy release Drier to large earthquakes. The two automata have different nearest neighbor laws, one of which produces self-organized critical (SOC) behavior (PSD model) and the other which produces quasi-periodic large events (crack model). In the PSD model periods of accelerating energy release before large events are rare. In the crack model, many large events are preceded by periods of accelerating energy release. When compared to randomized event catalogs, accelerating energy release before large events occurs more often than random in the crack model but less often than random in the PSD model; it is easier to tell the crack and PSD model results apart from each other than to tell either model apart from a random catalog. The evolution of event sizes during the accelerating energy release sequences in all models is compared to that of observed sequences. The accelerating energy release sequences in the crack model consist of an increase in the rate of events of all sizes, consistent with observations from a small number of natural cases, however inconsistent with a larger number of cases in which there is an increase in the rate of only moderate-sized events. On average, no increase in the rate of events of any size is seen before large events in the PSD model.

Long-Term Prospective, Randomized, Controlled Study Using Repetitive Education at Six-Month Intervals and Monitoring for Adherence in Heart Failure Outpatients The REMADHE Trial

Background-The effectiveness of heart failure disease management proarams in patients under cardiologists` care over long-term follow-up is not established. Methods and Results-We investigated the effects of a disease management program with repetitive education and telephone monitoring on primary (combined death or unplanned first hospitalization and quality-of-life changes) and secondary end points (hospitalization, death, and adherence). The REMADHE [Repetitive Education and Monitoring for ADherence for Heart Failure] trial is a long-term randomized, prospective, parallel trial designed to compare intervention with control. One hundred seventeen patients were randomized to usual care, and 233 to additional intervention. The mean follow-up was 2.47 +/- 1.75 years, with 54% adherence to the program. In the intervention group, the primary end point composite of death or unplanned hospitalization was reduced (hazard ratio, 0.64; confidence interval, 0.43 to 0.88; P=0.008), driven by reduction in hospitalization. The quality-of-life questionnaire score improved only in the intervention group (P<0.003). Mortality was similar in both groups. Number of hospitalizations (1.3 +/- 1.7 versus 0.8 +/- 1.3, P<0.0001), total hospital days during the follow-up (19.9 +/- 51 versus 11.1 +/- 24 days, P<0.0001), and the need for emergency visits (4.5 +/- 10.6 versus 1.6 +/- 2.4, P<0.0001) were lower in the intervention group. Beneficial effects were homogeneous for sex, race, diabetes and no diabetes, age, functional class, and etiology. Conclusions-For a longer follow-up period than in previous studies, this heart failure disease management program model of patients under the supervision of a cardiologist is associated with a reduction in unplanned hospitalization, a reduction of total hospital days, and a reduced need for emergency care, as well as improved quality of life, despite modest program adherence over time. (Circ Heart Fail. 2008;1:115-124.)

Modelling of cold-formed purlin-sheeting systems .2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold-formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its goon con elation with experimental results. (C) 1997 Elsevier Science Ltd.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as ail alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models. (C) 1997 Society for Mathematical Biology.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

An aggregate sales model for consumer durables incorporating a time-varying mean replacement age

Forecasting category or industry sales is a vital component of a company's planning and control activities. Sales for most mature durable product categories are dominated by replacement purchases. Previous sales models which explicitly incorporate a component of sales due to replacement assume there is an age distribution for replacements of existing units which remains constant over time. However, there is evidence that changes in factors such as product reliability/durability, price, repair costs, scrapping values, styling and economic conditions will result in changes in the mean replacement age of units. This paper develops a model for such time-varying replacement behaviour and empirically tests it in the Australian automotive industry. Both longitudinal census data and the empirical analysis of the replacement sales model confirm that there has been a substantial increase in the average aggregate replacement age for motor vehicles over the past 20 years. Further, much of this variation could be explained by real price increases and a linear temporal trend. Consequently, the time-varying model significantly outperformed previous models both in terms of fitting and forecasting the sales data. Copyright (C) 2001 John Wiley & Sons, Ltd.

A formal model of real-time program compilation

Program compilation can be formally defined as a sequence of equivalence-preserving transformations, or refinements, from high-level language programs to assembler code, Recent models also incorporate timing properties, but the resulting formalisms are intimidatingly complex. Here we take advantage of a new, simple model of real-time refinement, based on predicate transformer semantics, to present a straightforward compilation formalism that incorporates real-time constraints. (C) 2002 Elsevier Science B.V. All rights reserved.

Biaxial failure model for fiber reinforced concrete

Steel fiber reinforced concrete (SFRC) is widely applied in the construction industry. Numerical elastoplastic analysis of the macroscopic behavior is complex. This typically involves a piecewise linear failure curve including corner singularities. This paper presents a single smooth biaxial failure curve for SFRC based on a semianalytical approximation. Convexity of the proposed model is guaranteed so that numerical problems are avoided. The model has sufficient flexibility to closely match experimental results. The failure curve is also suitable for modeling plain concrete under biaxial loading. Since this model is capable of simulating the failure states in all stress regimes with a single envelope, the elastoplastic formulation is very concise and simple. The finite element implementation is developed to demonstrate the conciseness and the effectiveness of the model. The computed results display good agreement with published experimental data.

Collecting system percutaneous access using real-time tracking sensors: first pig model in vivo experience

Purpose: Precise needle puncture of the renal collecting system is an essential but challenging step for successful percutaneous nephrolithotomy. We evaluated the efficiency of a new real-time electromagnetic tracking system for in vivo kidney puncture. Materials and Methods: Six anesthetized female pigs underwent ureterorenoscopy to place a catheter with an electromagnetic tracking sensor into the desired puncture site and ascertain puncture success. A tracked needle with a similar electromagnetic tracking sensor was subsequently navigated into the sensor in the catheter. Four punctures were performed by each of 2 surgeons in each pig, including 1 each in the kidney, middle ureter, and right and left sides. Outcome measurements were the number of attempts and the time needed to evaluate the virtual trajectory and perform percutaneous puncture. Results: A total of 24 punctures were easily performed without complication. Surgeons required more time to evaluate the trajectory during ureteral than kidney puncture (median 15 seconds, range 14 to 18 vs 13, range 11 to 16, p ¼ 0.1). Median renal and ureteral puncture time was 19 (range 14 to 45) and 51 seconds (range 45 to 67), respectively (p ¼ 0.003). Two attempts were needed to achieve a successful ureteral puncture. The technique requires the presence of a renal stone for testing. Conclusions: The proposed electromagnetic tracking solution for renal collecting system puncture proved to be highly accurate, simple and quick. This method might represent a paradigm shift in percutaneous kidney access techniques

Collecting system percutaneous access using real-time tracking sensors: first pig model in vivo experience

Purpose: Precise needle puncture of the renal collecting system is an essential but challenging step for successful percutaneous nephrolithotomy. We evaluated the efficiency of a new real-time electromagnetic tracking system for in vivo kidney puncture. Materials and Methods: Six anesthetized female pigs underwent ureterorenoscopy to place a catheter with an electromagnetic tracking sensor into the desired puncture site and ascertain puncture success. A tracked needle with a similar electromagnetic tracking sensor was subsequently navigated into the sensor in the catheter. Four punctures were performed by each of 2 surgeons in each pig, including 1 each in the kidney, middle ureter, and right and left sides. Outcome measurements were the number of attempts and the time needed to evaluate the virtual trajectory and perform percutaneous puncture. Results: A total of 24 punctures were easily performed without complication. Surgeons required more time to evaluate the trajectory during ureteral than kidney puncture (median 15 seconds, range 14 to 18 vs 13, range 11 to 16, p ¼ 0.1). Median renal and ureteral puncture time was 19 (range 14 to 45) and 51 seconds (range 45 to 67), respectively (p ¼ 0.003). Two attempts were needed to achieve a successful ureteral puncture. The technique requires the presence of a renal stone for testing. Conclusions: The proposed electromagnetic tracking solution for renal collecting system puncture proved to be highly accurate, simple and quick. This method might represent a paradigm shift in percutaneous kidney access techniques.