Home About us Contact
|
Home About us Contact | ||
|
|
||
Negative Binomial Distribution (negative + binomial_distribution)
Selected AbstractsDesigning Accurate Control Charts Based on the Geometric and Negative Binomial DistributionsQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 8 2005Neil C. Schwertman Abstract Attribute control charts are used effectively to monitor for process change. Their accuracy can be improved by judiciously selecting the sample size. The required sample sizes to achieve accuracy can be quite restrictive, especially when the nominal proportions of non-conforming units are quite small. The usual attribute control chart has a set sample size and the number of non-conforming units in the sample is plotted. If, instead of setting a specific sample size the number of non-conforming units is set, an alternative monitoring process is possible. Specifically, the cumulative count of conforming (CCC- r) control chart is a plot of the number of units that must be tested to find the rth non-conforming unit. These charts, based on the geometric and negative binomial distributions, are often suggested for monitoring very high quality processes. However, they can also be used very efficiently to monitor processes of lesser quality. This procedure has the potential to find process deterioration more quickly and efficiently. Xie et al. (Journal of Quality and Reliability Management 1999; 16(2):148,157) provided tables of control limits for CCC- r charts for but focused mainly on high-quality processes and the tables do not include any assessments of the risk of a false alarm or the reliability of detecting process change. In this paper, these tables are expanded for processes of lesser quality and include such assessments using the number of expected monitoring periods (average run lengths (ARLs)) to detect process change. Also included is an assessment of the risk of a false alarm, that is, a false indication of process deterioration. Such assessments were not included by Xie et al. but are essential for the quality engineer to make sound decisions. Furthermore, a hybrid of the control charts based on the binomial, geometric and negative binomial distributions is proposed to monitor for process change. Copyright © 2005 John Wiley & Sons, Ltd. [source] Predicting global abundance of a threatened species from its occurrence: implications for conservation planningDIVERSITY AND DISTRIBUTIONS, Issue 1 2009Marcos S. L. Figueiredo Abstract Aim, Global abundance is an important characteristic of a species that is correlated with geographical distribution and body size. Despite its importance these estimates are not available since reliable field estimates are either expensive or difficult to obtain. Based on the relationship between a species' local abundance and distribution, some authors propose that abundance can be obtained through spatial distribution data from maps plotted at different scales. This has never been tested over the entire geographical range of a species. Thus, the aim of this study was to estimate global abundance of the Neotropical primate Brachyteles hypoxanthus (northern muriqui) and compare the results with available field estimates. Location, From southern Bahia to Minas Gerais and Espírito Santo states, in the Brazilian Atlantic rain forest. Methods, We compiled 25 recent occurrence localities of B. hypoxanthus and plotted them in grid cells of five different sizes (1, 25, 50, 75 and 100 km per side) to evaluate the performance and accuracy of abundance estimates over a wide range of scales. The abundance estimates were obtained by the negative binomial distribution (NBD) method and corrected by average group size to take into account primate social habits. To assess the accuracy of the method, the predicted abundances were then compared to recent independent field estimates. Results, The NBD estimates were quite accurate in predicting B. hypoxanthus global abundance, once the gregarious habits of this species are taken into account. The predicted abundance estimates were not statistically different from those obtained from field estimates. Main conclusions, The NBD method seems to be a quick and reliable approach to estimate species abundance once several limiting factors are taken into account, and can greatly impact conservation planning, but further applications in macroecological and ecological theory testing needs improvement of the method. [source] Measures, perceptions and scaling patterns of aggregated species distributionsECOGRAPHY, Issue 1 2010Cang Hui Non-random (aggregated) species distributions arise from habitat heterogeneity and nonlinear biotic processes. A comprehensive understanding of the concept of aggregation, as well as its measurement, is pivotal to our understanding of species distributions and macroecological patterns. Here, using an individual-based model, we analyzed opinions on the concept of aggregation from the public and experts (trained ecologists), in addition to those calculated from a variety of aggregation indices. Three forms of scaling patterns (logarithmic, power-law and lognormal) and four groups of scaling trajectories emerged. The experts showed no significant difference from the public, although with a much lower deviation. The public opinion was partially influenced by the abundance of individuals in the spatial map, which was not found in the experts. With the increase of resolution (decrease of grain), aggregation indices showed a general trend from significantly different to significantly similar to the expert opinion. The over-dispersion index (i.e. the clumping parameter k in the negative binomial distribution) performed, at certain scales, as the closest index to the expert opinion. Examining performance of aggregation measures from different groups of scaling patterns was proposed as a practical way of analyzing spatial structures. The categorization of the scaling patterns of aggregation measures, as well as their over- and in-sensitivity towards spatial structures, thus not only provides a potential solution to the modifiable areal unit problem, but also unveils the interrelationship among the concept, measures and perceptions of aggregated species distributions. [source] The role of resources and natural enemies in determining the distribution of an insect herbivore populationECOLOGICAL ENTOMOLOGY, Issue 2 2001Iain S. Williams Summary 1. Both resources and natural enemies can influence the distribution of a herbivore. The ideal free distribution predicts that herbivores distribute themselves to optimise utilisation of resources. There is also evidence of herbivores seeking out refuges that reduce natural enemy attack (enemy-free space). Which of these theories predominates in a thistle,tephritid Terellia ruficauda (Diptera: Tephritidae),parasitoid interaction is examined. 2. The plant, Cirsium palustre, had a contagious distribution approximated by the negative binomial distribution. Terellia ruficauda foraged preferentially and oviposited on isolated plants although its larvae gained neither nutritional benefit nor reduced natural enemy pressure from such behaviour. 3. Parasitoids of T. ruficauda foraged and oviposited more frequently on isolated than on crowded T. ruficauda, resulting in inverse density-dependent parasitoid attack at all spatial scales examined. Neither the herbivore nor natural enemies distributed themselves according to the predictions of the ideal free distribution and the herbivore did not oviposit to reduce natural enemy attack. 4. Extrapolating from the theoretical predictions of the ideal free distribution and enemy-free space to the field requires considerable caution. Terellia ruficauda and its parasitoids appear to select their oviposition sites to spread the risk of losses through factors (e.g. mammal herbivory) that may damage dense clusters of C. palustre. [source] Distributional Patterns of Diatoms and Limnodrilus Oligochaetes in a Kenyan Dry Streambed Following the 1999,2000 Drought ConditionsINTERNATIONAL REVIEW OF HYDROBIOLOGY, Issue 2 2005Jude M. Mathooko Abstract Drought is a natural phenomenon experienced by many intermittent and also seasonal lotic systems. It has diverse effects on the structure and distribution of biological communities through habitat transition from wetted to terrestrial conditions. The Njoro River, a tropical stream, was drought-stressed between late 1999 and mid 2000, providing an opportunity to sample and describe the distributional patterns of diatoms and Limnodrilus oligochaetes in the vertical sediment profile. The dispersion of Limnodrilus oligochaetes with sediment depth profile varied from quasi-random (i.e. exponent k of the negative binomial distribution >2.0 or <0) at the surface to strong aggregation (0 < k < 1.0) in the deeper sediments. Diatoms were heterogenous, with most species contributing less than 1% of all the diatoms collected from the riverbed. Contagious dispersion was a common feature among the diatom species. The distribution of Fragilaria ulna was largely quasi-random in all sites, with Nitzschia amphibia and Cocconeis placentula demonstrating quasi-random distribution in the Kerma vertical sediment profile. Escape from stranding to deeper sediment strata as the drought progressed was not a universal response among the diatom species. Our results showed that drought-stress altered the structure of biological assemblages and also emphasized the need for the management of tropical lotic systems and their catchments for flow permanence. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Predicting abundance from occupancy: a test for an aggregated insect assemblageJOURNAL OF ANIMAL ECOLOGY, Issue 3 2003M. Warren Summary 1The ubiquitous, positive abundance-occupancy relationship is of potential value to conservation and pest management because of the possibility of using it to predict species abundance from occupancy measures. 2He & Gaston (2000a) developed a model, and a parameterization method, for the prediction of abundance from occupancy based on the negative binomial distribution. There are to date few empirical tests of either the estimation method or model. Here we conduct such a test in a field-based mesocosm experiment using a Drosophilidae assemblage associated with decaying fruit. 3With individual (and groups of) fruit as minimum mapping units, abundance estimates derived using the parameterization method of the He-Gaston model differed significantly from measured values, and were least accurate for the most abundant species. 4Substitution of k -values corrected for species density in the model did not improve abundance predictions significantly. However, substitution of k -values calculated directly from the negative binomial distribution yielded highly accurate abundance predictions. 5Although the distribution of fly species did not deviate significantly from the negative binomial distribution, and the finest possible minimum mapping units were used (individual fruit), the parameterization method in the He-Gaston model consistently underestimated the abundance of species in the assemblage because individuals were very highly aggregated within fruit. 6Because of its potential importance, this model and parameterization method require further exploration at fine scales, commonly represented by individual habitat units, for highly aggregated species. The incorporation of spatially explicit information may provide a means of improving abundance predictions in this regard. [source] Sampling plan for the coffee leaf miner Leucoptera coffeella with sex pheromone trapsJOURNAL OF APPLIED ENTOMOLOGY, Issue 6 2008T. Bacca Abstract The population density of the coffee leaf miner Leucoptera coffeella (Guérin-Méneville & Perrottet) (Lep., Lyonetiidae) can be estimated using pheromone traps in coffee fields as male capture reflects this pest damage based on previous correlational study. However, the spatial distribution of pheromone traps and their density are necessary to optimize the sampling procedure with pheromone traps. Therefore, the objectives of the present study were to determine the pheromone trap density required per hectare to sample coffee leaf miner populations and to determine the spatial distribution of the males of this pest species. The males were sampled every 8 days in 12 consecutive evaluations. Taylor's power law and frequency distributions were used to recognize the distribution of the male capture data, which followed a negative binomial distribution. A common K was obtained, allowing the establishment of a single conventional sampling plan for the 12 fields investigated. The adjusted sampling plan requires eight traps in an area of 30 ha for a 25% precision error. Kriging-generated maps allowed the simulation of male captures for 8, 12 and 20 traps per 30 ha and the results were compared with those obtained with absolute sampling resulting in R2 -values of 0.30, 0.57 and 0.60 respectively. The traps were able to identify the more highly infested areas within the field and are a precise and efficient tool for sampling populations of L. coffeella. [source] Interspecific variation in primary seed dispersal in a tropical forestJOURNAL OF ECOLOGY, Issue 4 2008Helene C. Muller-Landau Summary 1We investigated the relationships of seed size, dispersal mode and other species characteristics to interspecific variation in mean primary seed dispersal distances, mean annual seed production per unit basal area, and clumping of seed deposition among 41 tropical tree species on Barro Colorado Island, Panama. 2A hierarchical Bayesian model incorporating interannual variation in seed production was used to estimate seed dispersal, seed production, and clumping of seed rain for each species from 19 years of data for 188 seed traps on a 50-ha plot in which all adult trees were censused every 5 years. 3Seed dispersal was modelled as a two-dimensional Student's T distribution with the degrees of freedom parameter fixed at 3, interannual variation in seed production per basal area was modelled as a lognormal, and the clumping of seed rain around its expected value was modelled as a negative binomial distribution. 4There was wide variation in seed dispersal distances among species sharing the same mode of seed dispersal. Seed dispersal mode did not explain significant variation in seed dispersal distances, but did explain significant variation in clumping: animal-dispersed species showed higher clumping of seed deposition. 5Among nine wind-dispersed species, the combination of diaspore terminal velocity, tree height and wind speed in the season of peak dispersal explained 40% of variation in dispersal distances. Among 31 animal-dispersed species, 20% of interspecific variation in dispersal distances was explained by seed mass (a negative effect) and tree height (a positive effect). 6Among all species, seed mass, tree height and dispersal syndrome explained 28% of the variation in mean dispersal distance and seed mass alone explained 45% of the variation in estimated seed production per basal area. 7Synthesis. There is wide variation in patterns of primary seed rain among tropical tree species. Substantial proportions of interspecific variation in seed production, seed dispersal distances, and clumping of seed deposition are explained by relatively easily measured plant traits, especially dispersal mode, seed mass, and tree height. This provides hope for trait-based generalization and modelling of seed dispersal in tropical forests. [source] Industry Characteristics Linked to Establishment Concentrations in Nonmetropolitan AreasJOURNAL OF REGIONAL SCIENCE, Issue 2 2000Yunsoo Kim In this paper we investigate industry characteristics associated with the clustering of establishments in three-digit SIC manufacturing industries in nonmetropolitan areas. The dispersion parameter k of the negative binomial distribution is selected as the measure of industry spatial concentration. Associations between industry characteristics and spatial concentration are investigated using OLS regression analysis. Our findings indicate that the spatial clustering of establishments is positively related to industry average establishment size, reliance on natural resource inputs, labor intensity, cost shares of professional and technical employees, and cost shares of low-skilled workers. Agglomeration is negatively related to multiplant structure, employment in precision production, and reliance on local product and input markets. [source] Distributional differences of the impact factor in the sciences versus the social sciences: An analysis of the probabilistic structure of the 2005 journal citation reportsJOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 9 2008Stephen J. Bensman This paper examines the probability structure of the 2005 Science Citation Index (SCI) and Social Sciences Citation Index (SSCI) Journal Citation Reports (JCR) by analyzing the Impact Factor distributions of their journals. The distribution of the SCI journals corresponded with a distribution generally modeled by the negative binomial distribution, whereas the SSCI distribution fit the Poisson distribution modeling random, rare events. Both Impact Factor distributions were positively skewed,the SCI much more so than the SSCI,indicating excess variance. One of the causes of this excess variance was that the journals highest in the Impact Factor in both JCRs tended to class in subject categories well funded by the National Institutes of Health. The main reason for the SCI Impact Factor distribution being more skewed than the SSCI one was that review journals defining disciplinary paradigms play a much more important role in the sciences than in the social sciences. [source] Multilevel modelling of the number of property crimes: household and area effectsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 2 2006Andromachi Tseloni Summary., This study examines household and area effects on the incidence of total property crimes and burglaries and thefts. It uses data from the 2000 British Crime Survey and the 1991 UK census small area statistics. Results are obtained from estimated random-effects multilevel models, with an assumed negative binomial distribution of the dependent variable. Both household and area characteristics, as well as selected interactions, explain a significant portion of the variation in property crimes. There are also a large number of significant between-area random variances and covariances of household characteristics. The estimated fixed and random effects may assist in advancing victimization theory. The methods have potential for developing a better understanding of factors that give rise to crime and so assist in framing crime prevention policy. [source] Seasonal dynamics, dispersion, sequential sampling plans and treatment thresholds for the citrus leafminer, Phyllocnistis citrella Stainton (Lepidoptera: Gracillariidae), in a mature lemon block in coastal New South Wales, AustraliaAUSTRALIAN JOURNAL OF ENTOMOLOGY, Issue 3 2008Zhong Min Liu Abstract, Studies of citrus leafminer in a coastal orchard in NSW, Australia indicated that an increase in abundance to about one mine per flush was followed during the midseason flush by a rapid increase in population that was related to an increase in the percentage of leaves infested within flushes and the number of mines per leaf. The fits of frequency distributions and Iwao's patchiness regression indicated that populations were highly contagious initially, and as the exponent k of the negative binomial distribution increased with increasing population density, the distribution approached random. Concurrently, the coefficient of variation of mines per flush (which was strongly related to the proportion of un-infested flushes) decreased to about unity as the proportion of un-infested flushes reached zero and fell further as the number of mines per flush increased. Both numerative and binomial sequential sampling plans were developed using a decision threshold based on 1.2 mines per flush. The binomial sampling plan was based on a closely fitting model of the functional relationship between mean density and proportion of infested flushes. Functional relationships using the parameters determined from Iwao's patchiness regression and Taylor's power law were equally satisfactory, and one based on the negative binomial model also fitted well, but the Poisson model did not. The three best fitting models indicated that a decision threshold of 1.2 mines per flush was equivalent to 50% of flushes infested. From a practical point of view, the transition from 25% infestation of flushes through 50% is so rapid that it may be prudent to take action when the 25% level is reached; otherwise, the 50% may be passed before the crop is checked again. For valuable nursery stock should infestation be detected in spring, it may be advisable to apply prophylactic treatment as the midseason flush starts. [source] A Bayesian Long-term Survival Model Parametrized in the Cured FractionBIOMETRICAL JOURNAL, Issue 3 2009Mário de Castro Abstract The main goal of this paper is to investigate a cure rate model that comprehends some well-known proposals found in the literature. In our work the number of competing causes of the event of interest follows the negative binomial distribution. The model is conveniently reparametrized through the cured fraction, which is then linked to covariates by means of the logistic link. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis in the proposed model. The procedure is illustrated with a numerical example. [source] Is optimal foraging a realistic expectation in orb-web spiders?ECOLOGICAL ENTOMOLOGY, Issue 4 2009WILL EDWARDS Abstract 1.,Explanations for web relocation invoking optimal foraging require reliable differentiation between individual sites and overall habitat quality. We characterised natural conditions of resource variability over 20 days in artificial webs of the orb-web spider Gasteracantha fornicata to examine this requirement. 2.,Variability in catch success was high. Day-to-day catch success in 90% (18/20) catch sites fitted negative binomial distributions, whereas 10% fitted Poisson distributions. Considered across trap sites (overall habitat), variance in catch success increased proportionally faster than the mean (i.e. Taylor's Power Law, variance = 0.54mean1.764). 3.,We compared the confidence intervals for the expected cumulative catch in randomly drawn sequential samples from a frequency distribution representing the overall habitat (based on the parameters for Taylor's power law) and the frequency distribution of expected cumulative catch within each individual catch site [via randomisation based on the mean and negative binomial exponent (k)]. 4.,In all cases and across all sample sizes, median values for the power to differentiate habitat and catch sites never exceeded 0.2, suggesting that principles involved in optimal foraging, if operating, must be accompanied by a very high degree of uncertainty. 5.,Under conditions of high resource variability, many days must be spent in a single catch site if movement decisions are based on an ability to differentiate current catch site from overall habitat. Empirical evidence suggests this is never met. This may explain why proximal mechanisms that illicit quickly resolved behavioural responses have been more successful in describing web relocation patterns than those associated with optimal foraging. [source] Dispersion patterns of parasites in 0+ year three-spined sticklebacks: a cross population comparisonJOURNAL OF FISH BIOLOGY, Issue 6 2002M. Kalbe Two ciliates and 16 metazoan parasites were identified in 434 0+ year three-spined sticklebacks Gasterosteus aculeatus collected from two small rivers and four lakes located in Schleswig-Holstein, Germany. By repeated sampling and analysis of dispersion patterns of six frequently occurring parasites no consistent evidence was found for mortality induced by a single parasite species. Linear log-variance to log-mean abundance ratios with slopes of c. 2 indicated negative binomial distributions for five of the six parasites. The numbers of these six parasites were combined as multiples of S.D. of each parasite species over all samples to form an ,individual parasitation index' (IPI), which showed that only in one locality a slight decrease in parasite burden occurred between September and April. In two of the lake populations, however, there was a distinct decline in the degree of dispersion in spring samples. This indicates that a combination of different species might cause parasite-induced host mortality, undetectable by patterns obtained from single species. There were differences in parasite diversity and intensity of infection among river compared to lake populations suggesting a role for parasites as selective agents in the ecological divergence of three-spined sticklebacks. [source] Designing Accurate Control Charts Based on the Geometric and Negative Binomial DistributionsQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 8 2005Neil C. Schwertman Abstract Attribute control charts are used effectively to monitor for process change. Their accuracy can be improved by judiciously selecting the sample size. The required sample sizes to achieve accuracy can be quite restrictive, especially when the nominal proportions of non-conforming units are quite small. The usual attribute control chart has a set sample size and the number of non-conforming units in the sample is plotted. If, instead of setting a specific sample size the number of non-conforming units is set, an alternative monitoring process is possible. Specifically, the cumulative count of conforming (CCC- r) control chart is a plot of the number of units that must be tested to find the rth non-conforming unit. These charts, based on the geometric and negative binomial distributions, are often suggested for monitoring very high quality processes. However, they can also be used very efficiently to monitor processes of lesser quality. This procedure has the potential to find process deterioration more quickly and efficiently. Xie et al. (Journal of Quality and Reliability Management 1999; 16(2):148,157) provided tables of control limits for CCC- r charts for but focused mainly on high-quality processes and the tables do not include any assessments of the risk of a false alarm or the reliability of detecting process change. In this paper, these tables are expanded for processes of lesser quality and include such assessments using the number of expected monitoring periods (average run lengths (ARLs)) to detect process change. Also included is an assessment of the risk of a false alarm, that is, a false indication of process deterioration. Such assessments were not included by Xie et al. but are essential for the quality engineer to make sound decisions. Furthermore, a hybrid of the control charts based on the binomial, geometric and negative binomial distributions is proposed to monitor for process change. Copyright © 2005 John Wiley & Sons, Ltd. [source] | |||||||||||||