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.

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.

Distribution of Aceria guerreronis and Neoseiulus baraki among and within coconut bunches in northeast Brazil

Aceria guerreronis Keifer (Acari: Eriophyidae) is considered a major pest of coconut in many countries in the Americas, Africa and parts of Asia. Neoseiulus baraki Athias-Henriot (Acari: Phytoseiidae) is one of the predatory mites most commonly found in association with A. guerreronis in parts of northeast Brazil. The objective of this work was to study the distribution of A. guerreronis and N. baraki among and within coconut bunches. The hypothesis was tested that A. guerreronis and N. baraki are homogenously distributed over the fruits in a bunch, independent of the fruits` age and position. Five collections of bunches, each corresponding to leaves 12-16 from apex (about 2-6 month-old), were conducted in each of three fields in northeastern Brazil, from February to October, 2007. A total of 1,986 fruits were examined. The number of mites, the percentage of fruits hosting them and the level of damage caused by A. guerreronis were evaluated. The highest density of A. guerreronis was observed on fruits of bunch 4 whereas the highest density of N. baraki was observed on bunch 5. Considering all fruits together, no significant differences were observed between densities of either A. guerreronis or N. baraki among the basal, median and apical thirds of the bunches. In younger bunches, fruits of the apical region tend to have lower densities of both mites than fruits of the basal region. This pattern, in association with a similar pattern for the percentage of fruits hosting N. baraki, suggests that the predator initially reaches the basal bunch region, from where it moves to the apical region. The results of the present study suggest that the pest population reduction in bunches older than bunch 4 could be due to (1) an effect of the predator, (2) reduction of the proportion of undamaged tissues amenable to attack, and/or (3) less favorable characteristics of the fruits to attack by A. guerreronis, as indicated by their increasing lignin content as they get older.

Modelling the potential distribution of the invasive tomato red spider mite, Tetranychus evansi (Acari: Tetranychidae)

Predicting the potential geographical distribution of a species is particularly important for pests with strong invasive abilities. Tetranychus evansi Baker & Pritchard, possibly native to South America, is a spider mite pest of solanaceous crops. This mite is considered an invasive species in Africa and Europe. A CLIMEX model was developed to predict its global distribution. The model results fitted the known records of T. evansi except for some records in dry locations. Dryness as well as excess moisture stresses play important roles in limiting the spread of the mite in the tropics. In North America and Eurasia its potential distribution appears to be essentially limited by cold stress. Detailed potential distribution maps are provided for T. evansi in the Mediterranean Basin and in Japan. These two regions correspond to climatic borders for the species. Mite establishment in these areas can be explained by their relatively mild winters. The Mediterranean region is also the main area where tomato is grown in open fields in Europe and where the pest represents a threat. According to the model, the whole Mediterranean region has the potential to be extensively colonized by the mite. Wide expansion of the mite to new areas in Africa is also predicted. Agricultural issues highlighted by the modelled distribution of the pest are discussed.

Distribution of Tetranychus evansi and its predator Phytoseiulus longipes (Acari : Tetranychidae, Phytoseiidae) in southern Brazil

Tetranychus evansi is an important pest of tomato in several countries. The predatory mite Phytoseiulus longipes has been found in association with it in Uruguaiana, State of Rio Grande do Sul, Brazil. The objective of this study was to evaluate the distribution of those two species in Uruguaiana region. Bi-weekly samples of plant parts were taken between January 28 and April 30, 2007 in Uruguaiana and five neighboring counties. Tetranychus evansi was found in all counties, but P. longipes was only found in Uruguaiana, mainly in the urban area. It is conceivable that such restricted distribution of P. longipes is due to its recent introduction to the region. Alternatively, unfavorable winter conditions could prevent its persistence, except in protected places. Buildings and vegetation characteristics of the urban area of Uruguaiana could moderate strong winds, intense rainfall and low temperatures that commonly occur in the area.

Biogeographic distribution of the phytoseiidae (Acari : Mesostigmata)

More than 1982 species in 90 genera were included in an analysis of the biogeography of the Phytoseiidae, a family of predatory mites. Seven biogeographic regions were taken into account: Nearctic, Neotropical, Ethiopian, West Palaearctic, East Palaearctic, Oriental, and Australasian. The number of species was particularly high in the Neotropical, Oriental, and West Palaearctic regions. These regions also present the highest levels of species endemism. The number of genera was quite similar in all regions except for the Neotropics, which also had a high level of endemism. The possible Gondwanian (Neotropical, Ethiopian, Australasian, and Oriental regions) origin of the Phytoseiidae, most probably in the Neotropics, and their possible radiation to Laurasia (Nearctic, West Palaearctic, and East Palaearctic regions) are discussed. The comparison between genera and species in the different biogeographic regions indicate the importance of both dispersal and vicariance events in the evolution of the group. Dispersal is assumed to have been most important between Neotropical and Nearctic regions and between East Palaearctic and Oriental regions, whereas vicariance could have been the dominating process between Australasian, Ethiopian, and Oriental regions, as well as between West and East Palaearctic regions. A parsimony analysis of endemicity showed the Neotropical and the Nearctic regions to be isolated from the other regions. This is certainly due to a diversification after the continents drifted apart and then a high dispersal between Nearctic and Neotropical regions. Different phylogenetic hypotheses and scenarios are proposed for each subfamily based on the results obtained and further investigations are proposed. (C) 2008 The Linnean Society of London.

Distribution and storage characterization of soil solution for drip irrigation

The increased use of marginal quality water with drip irrigation requires sound fertigation practices that reconcile environmental concerns with viable crop production objectives. We conducted experiments to characterize dynamics and patterns of soil solution within wet bulb formed by drip irrigation. Time-domain reflectometry probes were used to monitor the distribution of potassium nitrate (KNO(3)) and water distribution from drippers discharging at constant flow rates of 2, 4 and 8 L h(-1) in soil-filled containers. Considering results from different profiles, we observed greater solute storage near the dripper decreasing gradually towards the wetting front. About half of the applied KNO(3) solution (48%) was stored in the first layer (0-0.10 m) for all experiments, 29% was stored in the next layer (0.10-0.20 m). Comparing different dripper flow rates, we observed higher solution storage for 4 L h(-1), with 45, 53 and 47% of applied KNO(3) solution accumulating in the first layer (0-0.10 m) for dripper flow rates of 2, 4 and 8 L h(-1), respectively. The results suggest that based on the volume and frequency used in this experiment, it would be advantageous to apply small amounts of solution at more frequent intervals to reduce deep percolation losses of applied water and solutes.

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.

Spatial pattern of black spot incidence within citrus trees related to disease severity and pathogen dispersal

Guignardia citricarpa, the causal agent of citrus black spot, forms airborne ascospores on decomposing citrus leaves and water-spread conidia on fruits, leaves and twigs. The spatial pattern of diseased fruit in citrus tree canopies was used to assess the importance of ascospores and conidia in citrus black spot epidemics in Sao Paulo State, Brazil. The aggregation of diseased fruit in the citrus tree canopy was quantified by the binomial dispersion index (D) and the binary form of Taylor`s Power Law for 303 trees in six groves. D was significantly greater than 1 in 251 trees. The intercept of the regression line of Taylor`s Power Law was significantly greater than 0 and the slope was not different from 1, implying that diseased fruit was aggregated in the canopy independent of disease incidence. Disease incidence (p) and severity (S) were assessed in 2875 citrus trees. The incidence-severity relationship was described (R-2 = 88.7%) by the model ln(S) = ln(a) + bCLL(p) where CLL = complementary log-log transformation. The high severity at low incidence observed in many cases is also indicative of low distance spread of G. citricarpa spores. For the same level of disease incidence, some trees had most of the diseased fruit with many lesions and high disease severity, whereas other trees had most of the fruit with few lesions and low disease severity. Aggregation of diseased fruit in the trees suggests that splash-dispersed conidia have an important role in increasing the disease in citrus trees in Brazil.

Cattle Grazing Distribution and Efficacy of Strategic Mineral Mix Placement in Tropical Brazilian Pastures

A study was conducted in Brazil to identify factors affecting grazing distribution of yearling Nelore cross heifers and to evaluate the efficacy of placement of a salt-mineral mix away from water to improve uniformity of grazing. Two pastures (25 ha and 42 ha) were evaluated for four 15-d sessions. Mineral mix was placed 590 m to 780 m from water during two sessions and at water for two sessions. Stubble heights were measured at the beginning and end of each session in 1-ha subunits of each pasture. Cattle locations were recorded oil clay 13 and 14 of each session by horseback observers. Heifers avoided areas with a preponderance of forbs and taller grass (P < 0.001). For the first 15 days of the study cattle avoided subunits farther from water. Thereafter, horizontal distance from water had no affect on grazing use (P > 0.10). Stubble height reduction was more uniform (P < 0.05) when the mineral mix was Lit water compared to away from water. In contrast, heifers spent less time farther from water when Mineral mix was placed at water (P = 0.02) based Oil Visual observations. Strategic placement of a salt-mineral mix away from water does not appear to be a reliable tool to improve cattle grazing distribution in humid tropical pastures from 25 ha to 45 ha in size.

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.

Silicon distribution and accumulation in shoot tissue of the tropical forage grass Brachiaria brizantha

Silicon (Si) accumulation in organs and cells is one of the most prominent characteristics of plants of the family Poaceae. Many species from this family are used as forage plants for animal feeding. The present study investigates in Brachiaria brizantha (Hochst. ex A. Rich.) Stapf. cv. Marandu: (1) the dry matter production and Si content in shoot due to soil Si fertilizations; (2) the Si distribution among shoot parts; and (3) the silica deposition and localization in leaves. Plants of B. brizantha cv. Marandu were grown under contrasting Si supplies in soil and nutrient solution. Silica deposition and distribution in grass leaf blades were observed using light microscope and scanning electron microscope equipped with an energy dispersive X-ray spectrometer (SEM-EDXS). Silicon concentration in the B. brizantha shoot increased according to the Si supply. Silicon in grass leaves decreased following the order: mature leaf blades > recently expanded leaf blades > non-expanded leaf blades. Silicon accumulates mainly on the upper (adaxial) epidermis of the grass leaf blades and, especially, on the bulliform cells. The Si distribution on adaxial leaf blade surface is non uniform and reflects a silica deposition exclusively on the cell wall of bulliform cells.

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.