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.

Impacts of land-use pattern on soil water-content variability on the Loess Plateau of China

Long-term vegetation restoration carried out on the slopes of the Loess Plateau of China employed different spatial and temporal land-use patterns but very little is known about the effects of these patterns on soil water-content variability. For this study the small Donggou catchment was selected to investigate soil water-content distributions for three spatial scales, including the entire catchment area, sampling transects, and land-use systems. Gravimetric soil water contents were determined incrementally to a soil depth of 1.20 m, on 10 occasions from April to October, 2007, at approximately 20-day intervals. Results indicated that soil water contents were affected by the six land-use types, resulting in four distinct patterns of vertical distribution of soil moisture (uniform, increasing, decreasing, and fluctuating with soil depth). The soil water content and its variation were also influenced in a complex manner by five land-use patterns distributed along transects following the gradients of five similar slopes. These patterns with contrasting hydrological responses in different components, such as forage land (alfalfa)-cropland-shrubland or shrubland-grassland (bunge needlegrass)-cropland-grassland, showed the highest soil water-content variability. Soil water at the catchment scale exhibited a moderate variability for each measurement date, and the variability of soil water content decreased exponentially with increasing soil water content. The minimum sample size for accurate data for use in a hydrological model for the catchment, for example, required many more samples for drier (69) than for wet (10) conditions. To enhance erosion and runoff control, this study suggested two strategies for land management: (i) to create a mosaic pattern by land-use arrangement that located units with higher infiltration capacities downslope from those with lower soil infiltrabilities; and (ii) raising the soil-infiltration capacity of units within the spatial mosaic pattern where possible.

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.

Pupal Development of Ceratitis capitata (Diptera: Tephritidae) and Diachasmimorpha longicaudata (Hymenoptera: Braconidae) at Different Moisture Values in Four Soil Types

This study aimed to evaluate adult emergence and duration of the pupal stage of the Mediterranean fruit fly, Ceratitis capitata (Wiedemann), and emergence of the fruit fly parasitoid, Diachasmimorpha longicaudata (Ashmead), under different moisture conditions in four soil types, using soil water matric potential Pupal stage duration in C capitata was influenced differently for males and females In females, only soil type affected pupal stage duration, which was longer in a clay soil In males, pupal stage duration was individually influenced by moisture and soil type, with a reduction in pupal stage duration in a heavy clay soil and in a sandy clay, with longer duration in the clay soil As allude potential decreased, duration of the pupal stage of C capitata males increased, regardless of soil type C capitata emergence was affected by moisture, regardless of soil type, and was higher in drier soils The emergence of D longicaudata adults was individually influenced by soil type and moisture factors, and the number of emerged D longicaudata adults was three times higher in sandy loam and lower in a heavy clay soil Always, the number of emerged adults was higher at higher moisture conditions C capitata and D longicaudata pupal development was affected by moisture and soil type, which may facilitate pest sampling and allow release areas for the parasitoid to be defined under field conditions.

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.

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.

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.

The dynamic of shrinkage/moisture content behavior determined during drying of microsamples for different kinds of wood

This article presents the results obtained from an experimental device designed for the accurate determination of wood/water relationship on microsamples. The moisture content of the sample is measured with a highly sensitive electronic microbalance and two dimensions of the sample are collected continuously without contact using high-speed laser scan micrometers. The whole device is placed in a climatic chamber. The microsamples investigated were prepared with a diamond wire saw. The unique ability of this device to work with small samples allowed normal, opposite, and reaction wood to be characterized separately. Experiments were carried out on three wood species (beech, spruce, and poplar). In the case of beech, a deviation from the linear relation between tangential shrinkage and moisture content between 40 and 20% is particularly noticeable for the first desorption. A localized collapse of ray cells could explain this result. Compared to normal wood, an important longitudinal shrinkage and a low tangential shrinkage were observed in compression wood of spruce. Both the tension wood and opposite wood of poplar exhibit a high longitudinal shrinkage, but no significant difference between the three types of wood is noticeable in the tangential direction.

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.