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.

Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each 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 to the modified martingale-type residual in log-Burr XII regression models with censored data.

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.

Formulating Mixed Models for Experiments, Including Longitudinal Experiments

Mixed models have become important in analyzing the results of experiments, particularly those that require more complicated models (e.g., those that involve longitudinal data). This article describes a method for deriving the terms in a mixed model. Our approach extends an earlier method by Brien and Bailey to explicitly identify terms for which autocorrelation and smooth trend arising from longitudinal observations need to be incorporated in the model. At the same time we retain the principle that the model used should include, at least, all the terms that are justified by the randomization. This is done by dividing the factors into sets, called tiers, based on the randomization and determining the crossing and nesting relationships between factors. The method is applied to formulate mixed models for a wide range of examples. We also describe the mixed model analysis of data from a three-phase experiment to investigate the effect of time of refinement on Eucalyptus pulp from four different sources. Cubic smoothing splines are used to describe differences in the trend over time and unstructured covariance matrices between times are found to be necessary.

Influence diagnostics for polyhazard models in the presence of covariates

In this paper, we present various diagnostic methods for polyhazard models. Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.

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.

On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 Elsevier B V All rights reserved

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

Production and carbon allocation in a clonal Eucalyptus plantation with water and nutrient manipulations

We examined resource limitations on growth and carbon allocation in a fast-growing, clonal plantation of Eucalyptus grandis x urophylla in Brazil by characterizing responses to annual rainfall, and response to irrigation and fertililization for 2 years. Productivity measures included gross primary production (GPP), total belowground carbon allocation (TBCA), bole growth, and net ecosystem production (NEP). Replicate plots within a single plantation were established at the midpoint of the rotation (end of year 3), with treatments of no additional fertilization or irrigation, heavy fertilization (to remove any nutrient limitation), irrigation (to remove any water limitation), and irrigation plus fertilization. Rainfall was unusually high in the first year (1769mm) of the experiment, and control plots had high rates of GPP (6.64 kg C m(-2) year(-1)), TBCA (2.14 kg C m(-2) year(-1)), and bole growth (1.81 kg C m(-2) year). Irrigation increased each of these rates by 15-17%. The second year of the experiment had average rainfall (1210 mm), and lower rainfall decreased production in control plots by 46% (GPP), 52% (TBCA), and 40% (bole growth). Fertilization treatments had neglible effects. The response to irrigation was much greater in the drier year, with irrigated plots exceeding the production in control plots by 83% (GPP), 239% (TBCA), and 24% (bole growth). Even though the rate of irrigation ensured no water limitation to tree growth, the high rainfall year showed higher production in irrigated plots for both GPP (38% greater than in drier year) and bole growth (23% greater). Varying humidity and supplies of water led to a range in NEP of 0.8-2.7 kg C m(-2) year. This difference between control and irrigated treatments, combined with differences between drier and wetter years, indicated a strong response of these Eucalyptus trees to both water supply and atmospheric humidity during the dry season. The efficiency of converting light energy into fixed carbon ranged from a low of 0.027 mol C to a high of 0.060 mol C per mol of absorbed photosynthetically active radiation (APAR), and the efficiency of bolewood production ranged from 0.78 to 1.98 g wood per MJ of APAR. Irrigation increased the efficiency of wood production per unit of water used from 2.55 kg wood m(-3) in the rainfed plot to 3.51 kg m(-3) in irrigated plots. Detailed information on the response of C budgets to environmental conditions and resource supplies will be necessary for accurate predictions of plantation yields across years and landscapes. (V) 2007 Elsevier B.V. All rights reserved.

Spatial portability of numerical models of leaf wetness duration based on empirical approaches

Leaf wetness duration (LWD) models based on empirical approaches offer practical advantages over physically based models in agricultural applications, but their spatial portability is questionable because they may be biased to the climatic conditions under which they were developed. In our study, spatial portability of three LWD models with empirical characteristics - a RH threshold model, a decision tree model with wind speed correction, and a fuzzy logic model - was evaluated using weather data collected in Brazil, Canada, Costa Rica, Italy and the USA. The fuzzy logic model was more accurate than the other models in estimating LWD measured by painted leaf wetness sensors. The fraction of correct estimates for the fuzzy logic model was greater (0.87) than for the other models (0.85-0.86) across 28 sites where painted sensors were installed, and the degree of agreement k statistic between the model and painted sensors was greater for the fuzzy logic model (0.71) than that for the other models (0.64-0.66). Values of the k statistic for the fuzzy logic model were also less variable across sites than those of the other models. When model estimates were compared with measurements from unpainted leaf wetness sensors, the fuzzy logic model had less mean absolute error (2.5 h day(-1)) than other models (2.6-2.7 h day(-1)) after the model was calibrated for the unpainted sensors. The results suggest that the fuzzy logic model has greater spatial portability than the other models evaluated and merits further validation in comparison with physical models under a wider range of climate conditions. (C) 2010 Elsevier B.V. All rights reserved.

Evaluation of FAO Penman-Monteith and alternative methods for estimating reference evapotranspiration with missing data in Southern Ontario, Canada

Grass reference evapotranspiration (ETo) is an important agrometeorological parameter for climatological and hydrological studies, as well as for irrigation planning and management. There are several methods to estimate ETo, but their performance in different environments is diverse, since all of them have some empirical background. The FAO Penman-Monteith (FAD PM) method has been considered as a universal standard to estimate ETo for more than a decade. This method considers many parameters related to the evapotranspiration process: net radiation (Rn), air temperature (7), vapor pressure deficit (Delta e), and wind speed (U); and has presented very good results when compared to data from lysimeters Populated with short grass or alfalfa. In some conditions, the use of the FAO PM method is restricted by the lack of input variables. In these cases, when data are missing, the option is to calculate ETo by the FAD PM method using estimated input variables, as recommended by FAD Irrigation and Drainage Paper 56. Based on that, the objective of this study was to evaluate the performance of the FAO PM method to estimate ETo when Rn, Delta e, and U data are missing, in Southern Ontario, Canada. Other alternative methods were also tested for the region: Priestley-Taylor, Hargreaves, and Thornthwaite. Data from 12 locations across Southern Ontario, Canada, were used to compare ETo estimated by the FAD PM method with a complete data set and with missing data. The alternative ETo equations were also tested and calibrated for each location. When relative humidity (RH) and U data were missing, the FAD PM method was still a very good option for estimating ETo for Southern Ontario, with RMSE smaller than 0.53 mm day(-1). For these cases, U data were replaced by the normal values for the region and Delta e was estimated from temperature data. The Priestley-Taylor method was also a good option for estimating ETo when U and Delta e data were missing, mainly when calibrated locally (RMSE = 0.40 mm day(-1)). When Rn was missing, the FAD PM method was not good enough for estimating ETo, with RMSE increasing to 0.79 mm day(-1). When only T data were available, adjusted Hargreaves and modified Thornthwaite methods were better options to estimate ETo than the FAO) PM method, since RMSEs from these methods, respectively 0.79 and 0.83 mm day(-1), were significantly smaller than that obtained by FAO PM (RMSE = 1.12 mm day(-1). (C) 2009 Elsevier B.V. All rights reserved.

Suitability of relative humidity as an estimator of leaf wetness duration

Leaf wetness duration (LWD) is a key parameter in agricultural meteorology since it is related to epidemiology of many important crops, controlling pathogen infection and development rates. Because LWD is not widely measured, several methods have been developed to estimate it from weather data. Among the models used to estimate LWD, those that use physical principles of dew formation and dew and/or rain evaporation have shown good portability and sufficiently accurate results, but their complexity is a disadvantage for operational use. Alternatively, empirical models have been used despite their limitations. The simplest empirical models use only relative humidity data. The objective of this study was to evaluate the performance of three RH-based empirical models to estimate LWD in four regions around the world that have different climate conditions. Hourly LWD, air temperature, and relative humidity data were obtained from Ames, IA (USA), Elora, Ontario (Canada), Florence, Toscany (Italy), and Piracicaba, Sao Paulo State (Brazil). These data were used to evaluate the performance of the following empirical LWD estimation models: constant RH threshold (RH >= 90%); dew point depression (DPD); and extended RH threshold (EXT_RH). Different performance of the models was observed in the four locations. In Ames, Elora and Piracicaba, the RH >= 90% and DPD models underestimated LWD, whereas in Florence these methods overestimated LWD, especially for shorter wet periods. When the EXT_RH model was used, LWD was overestimated for all locations, with a significant increase in the errors. In general, the RH >= 90% model performed best, presenting the highest general fraction of correct estimates (F(C)), between 0.87 and 0.92, and the lowest false alarm ratio (F(AR)), between 0.02 and 0.31. The use of specific thresholds for each location improved accuracy of the RH model substantially, even when independent data were used; MAE ranged from 1.23 to 1.89 h, which is very similar to errors obtained with published physical models for LWD estimation. Based on these results, we concluded that, if calibrated locally, LWD can be estimated with acceptable accuracy by RH above a specific threshold, and that the EXT_RH method was unsuitable for estimating LWD at the locations used in this study. (C) 2007 Elsevier B.V. All rights reserved.

Alternative Analytical Expressions for the General van Genuchten-Mualem and van Genuchten-Burdine Hydraulic Conductivity Models

The van Genuchten expressions for the unsaturated soil hydraulic properties, first published in 1980, are used frequently in various vadose zone flow and transport applications assuming a specific relationship between the m and n soil hydraulic parameters. By comparison, probably because of the complexity of the hydraulic conductivity equations, the more general solutions with independent m and n values are rarely used. We expressed the general van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity equations in terms of hypergeometric functions, which can be approximated by infinite series that converge rapidly for relatively large values of the van Genuchten-Mualem parameter n but only very slowly when n is close to one. Alternative equations were derived that provide very close approximations of the analytical results. The newly proposed equations allow the use of independent values of the parameters m and n in the soil water retention model of van Genuchten for subsequent prediction of the van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity models, thus providing more flexibility in fitting experimental pressure-head-dependent water content, theta(h), and hydraulic conductivity, K(h), or K(theta) data.

Forecasting fuel ethanol consumption in Brazil by time series models: 2006-2012

This article analysed scenarios for Brazilian consumption of ethanol for the period 2006 to 2012. The results show that if the country`s GDP sustains a 4.6% a year growth, domestic consumption of fuel ethanol could increase to 25.16 billion liters in this period, which is a volume relatively close to the forecasted gasoline consumption of 31 billion liters. At a lower GDP growth of 1.22% a year, gasoline consumption would be reduced and domestic ethanol consumption in Brazil would be no higher than 18.32 billion liters. Contrary to the current situation, forecasts indicated that hydrated ethanol consumption could become much higher than anhydrous consumption in Brazil. The former is being consumed in cars moved exclusively by ethanol and flex-fuel cars, successfully introduced in the country at 2003. Flex cars allow Brazilian consumers to choose between gasoline and hydrated ethanol and immediately switch to whichever fuel presents the most favourable relative price.

Does using stepwise variable selection to build sequential path analysis models make sense?

Causal inference methods - mainly path analysis and structural equation modeling - offer plant physiologists information about cause-and-effect relationships among plant traits. Recently, an unusual approach to causal inference through stepwise variable selection has been proposed and used in various works on plant physiology. The approach should not be considered correct from a biological point of view. Here, it is explained why stepwise variable selection should not be used for causal inference, and shown what strange conclusions can be drawn based upon the former analysis when one aims to interpret cause-and-effect relationships among plant traits.