The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

Bias-corrected Pearson estimating functions for Taylor`s power law applied to benthic macrofauna data

Estimation of Taylor`s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

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.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Macroscopic root water uptake distribution using a matric flux potential approach

Hydrological models featuring root water uptake usually do not include compensation mechanisms such that reductions in uptake from dry layers are compensated by an increase in uptake from wetter layers. We developed a physically based root water uptake model with an implicit compensation mechanism. Based on an expression for the matric flux potential (M) as a function of the distance to the root, and assuming a depth-independent value of M at the root surface, uptake per layer is shown to be a function of layer bulk M, root surface M, and a weighting factor that depends on root length density and root radius. Actual transpiration can be calculated from the sum of layer uptake rates. The proposed reduction function (PRF) was built into the SWAP model, and predictions were compared to those made with the Feddes reduction function (FRF). Simulation results were tested against data from Canada (continuous spring wheat [(Triticum aestivum L.]) and Germany (spring wheat, winter barley [Hordeum vulgare L.], sugarbeet [Beta vulgaris L.], winter wheat rotation). For the Canadian data, the root mean square error of prediction (RMSEP) for water content in the upper soil layers was very similar for FRF and PRF; for the deeper layers, RMSEP was smaller for PRF. For the German data, RMSEP was lower for PRF in the upper layers and was similar for both models in the deeper layers. In conclusion, but dependent on the properties of the data sets available for testing,the incorporation of the new reduction function into SWAP was successful, providing new capabilities for simulating compensated root water uptake without increasing the number of input parameters or degrading model performance.

Bayesian ratemaking procedure of crop insurance contracts with skewed distribution

Over the years, crop insurance programs became the focus of agricultural policy in the USA, Spain, Mexico, and more recently in Brazil. Given the increasing interest in insurance, accurate calculation of the premium rate is of great importance. We address the crop-yield distribution issue and its implications in pricing an insurance contract considering the dynamic structure of the data and incorporating the spatial correlation in the Hierarchical Bayesian framework. Results show that empirical (insurers) rates are higher in low risk areas and lower in high risk areas. Such methodological improvement is primarily important in situations of limited data.

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.

Occurrence and distribution of Vibrio parahaemolyticus in retail oysters in Sao Paulo State, Brazil

Vibrio parahaemolyticus is a potentially pathogenic bacterium that occurs naturally in estuarine environments worldwide, and is often associated with gastroenteritis in humans following consumption of raw bivalve mollusks, especially raw oysters. The occurrence of total and pathogenic V. parahaemolyticus in 74 samples of raw oysters collected in restaurants, supermarkets, groceries and beach huts in Sao Paulo State, was monitored between February 2006 and January 2007. Enumeration of V. parahaemolyticus was performed according to the most probable number (MPN) procedure. Five to ten typical colonies were selected from thiosulfate-citrate-bile salts-sucrose (TCBS) agar plates for confirmation by the presence of the species-specific gene tlh and the virulence genes tdh and trh by multiplex PCR. V. parahaemolyticus was detected in 100% of samples. The densities of total V. parahaemolyticus varied from 1.78 to 6.04 logio (MPN/g), with higher densities being detected in fall and summer, and lower densities in winter (P < 0.05). There was no statistical difference among densities of V parahaemolyticus regarding the site of collection. None of the 1943 V parahaemolyticus isolates contained tdh and/or trh. These data provide information for the assessment of exposure to V. parahaemolyticus in oysters consumed in Sao Paulo, State, Brazil. (C) 2010 Elsevier Ltd. All rights reserved.

Paste Residence Time in a Spouted Bed Dryer. IV: Effect of the Inert Particle Size Distribution

The residence time distribution and mean residence time of a 10% sodium bicarbonate solution that is dried in a conventional spouted bed with inert bodies were measured with the stimulus-response method. Methylene blue was used as a chemical tracer, and the effects of the paste feed mode, size distribution of the inert bodies, and mean particle size on the residence times and dried powder properties were investigated. The results showed that the residence time distributions could be best reproduced with the perfect mixing cell model or N = 1 for the continuous stirred tank reactor in a series model. The mean residence times ranged from 6.04 to 12.90 min and were significantly affected by the factors studied. Analysis of variance on the experimental data showed that mean residence times were affected by the mean diameter of the inert bodies at a significance level of 1% and by the size distribution at a level of 5%. Moreover, altering the paste feed from dripping to pneumatic atomization affected mean residence time at a 5% significance level. The dried powder characteristics proved to be adequate for further industrial manipulation, as demonstrated by the low moisture content, narrow range of particle size, and good flow properties. The results of this research are significant in the study of the drying of heat-sensitive materials because it shows that by simultaneously changing the size distribution and average size of the inert bodies, the mean residence times of a paste can be reduced by half, thus decreasing losses due to degradation.

Distribution of transferrin saturation in an Australian population: Relevance to the early diagnosis of hemochromatosis

Background & Aims: An elevated transferrin saturation is the earliest phenotypic abnormality in hereditary hemochromatosis. Determination of transferrin saturation remains the most useful noninvasive screening test for affected individuals, but there is debate as to the appropriate screening level. The aims of this study were to estimate the mean transferrin saturation in hemochromatosis heterozygotes and normal individuals and to evaluate potential transferrin saturation screening levels. Methods: Statistical mixture modeling was applied to data from a survey of asymptomatic Australians to estimate the mean transferrin saturation in hemochromatosis heterozygotes and normal individuals. To evaluate potential transferrin saturation screening levels, modeling results were compared with data from identified hemochromatosis heterozygotes and homozygotes. Results: After removal of hemochromatosis homozygotes, two populations of transferrin saturation were identified in asymptomatic Australians (P < 0.01). In men, 88.2% of the truncated sample had a lower mean transferrin saturation of 24.1%, whereas 11.8% had an increased mean transferrin saturation of 37.3%. Similar results were found in women, A transferrin saturation threshold of 45% identified 98% of homozygotes without misidentifying any normal individuals. Conclusions: The results confirm that hemochromatosis heterozygotes form a distinct transferrin saturation subpopulation and support the use of transferrin saturation as an inexpensive screening test for hemochromatosis. In practice, a fasting transferrin saturation of greater than or equal to 45% identifies virtually all affected homozygous subjects without necessitating further investigation of unaffected normal individuals.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

Flush air data system calibration using numerical simulation

The use of computational fluid dynamics simulations for calibrating a flush air data system is described, In particular, the flush air data system of the HYFLEX hypersonic vehicle is used as a case study. The HYFLEX air data system consists of nine pressure ports located flush with the vehicle nose surface, connected to onboard pressure transducers, After appropriate processing, surface pressure measurements can he converted into useful air data parameters. The processing algorithm requires an accurate pressure model, which relates air data parameters to the measured pressures. In the past, such pressure models have been calibrated using combinations of flight data, ground-based experimental results, and numerical simulation. We perform a calibration of the HYFLEX flush air data system using computational fluid dynamics simulations exclusively, The simulations are used to build an empirical pressure model that accurately describes the HYFLEX nose pressure distribution ol cr a range of flight conditions. We believe that computational fluid dynamics provides a quick and inexpensive way to calibrate the air data system and is applicable to a broad range of flight conditions, When tested with HYFLEX flight data, the calibrated system is found to work well. It predicts vehicle angle of attack and angle of sideslip to accuracy levels that generally satisfy flight control requirements. Dynamic pressure is predicted to within the resolution of the onboard inertial measurement unit. We find that wind-tunnel experiments and flight data are not necessary to accurately calibrate the HYFLEX flush air data system for hypersonic flight.