The Non-Central Negative Binomial Distribution

The non-central negative binomial distribution is derived by mixing the POISSON distribution with a certain BESSEL function distribution, or the negative binomial distribution with the POISSON distribution. Some properties of the distribution are discussed, including a characterization. The fitting of the distribution to some data are given together with the efficiency for various procedures of estimation.     

Distribution of the Sum of Independent Zero-Truncated Linear Function POISSON Random Variables

In this note, the distribution of the sum of independent zero-truncated linear function POISSON random variables is obtained. This distribution conforms, in special cases, to CACOULLOS (1972) and TATE and GOEN (1958). The distribution of the sum of zero-truncated BOREL-TANNER type variables is obtained as a special case.     

Bivariate POISSON Binomial Distributions

Three bivariate generalizations of the POISSON binomial distribution are introduced. The probabilities, moments, conditional distributions and regression functions for these distributions are obtained in terms of bipartitional polynomials. Recurrences for the probabilities and moments are also given. Parameter estimators are derived using the methods of moments and zero frequencies and the three distributions are fitted to some ecological data.     

On the KOLMOGOROV-SMIRNOV Test for the POISSON Distribution with Unknown Mean

The standard tables for the KOLMOGOROV -SMIRNOV test are valid only in the case of testing whether a set of observations is from a completely specified cumulative distribution, F₀(X), with all parameters known. If the parameters are unknown and must be estimated from the sample, then the tables are not valid. A table is given in this paper for use with the KOLMOGOROV -SMIRNOV statistic in the case of testing whether a set of observations is from the POISSON distribution with an unknown mean that must be estimated from the sample. The table is obtained from a Monte Carlo calculation.     

On the estimation of mean parameter with random number of observations on each unit

In this paper an attempt has been made to estimate the population parameter, mean, of a normal population when the number of observations taken on each unit is a random variable and is supposed to follow a Truncated POISSON Distribution.     

Some Applications of a Bivariate BOREL-TANNER Distribution

This paper considers the probability distribution of the number of customers served in the busy period of a single server queue with POISSON input and constant service time. Applications to traffic flow, semi-infinite discrete dam and branching processes are described. It is shown that in many situations the bivariate BOREL-TANNER distribution provides a better fit than the bivariate negative binomial distribution.     

影响入侵种反枝苋分布的环境因子分析及可能分布区预测

反枝苋(Amaranthus retroflexus)是苋属入侵种中发生频率最多、分布最广、危害最严重的杂草。基于反枝苋在世界范围内4 207个实际分布点及其对应的气候、地形和土壤3类要素28个环境因子的定量关系,利用主成分分析确定了影响其分布的主要环境因子,据此估测其中心可能分布区和最大可能分布区,并与实际分布点进行比较。结果表明:14个环境因子在决定反枝苋全球分布格局中起着重要作用。反枝苋中心分布区位于新西兰南部、澳大利亚东南部、南美洲北部少数地区、北美洲西北部及东南部部分地区、欧洲大部分地区和中国东南部,最大可能分布区位于南美洲中南部、北美洲大部分、非洲北部小部分、澳大利亚南部及北部少数区域、欧洲大部分地区和亚洲大部分地区及中国除西藏、青海、新疆、四川西部以外的地区。中心分布区的预测结果与实际分布点吻合较好,而最大分布区则过于广阔。     

花曲柳窄吉丁的空间分布

2004年4月~9月,在天津市大港区官港森林公园对花曲柳窄吉丁Agrilus planipennis的空间分布和垂直分布进行了调查研究,应用扩散系数(C)等6种指数法分析测定,确定了该虫在林地中的空间分布呈聚集分布,分布的基本成分是个体群。扩散蔓延规律为聚集型扩散。花曲柳窄吉丁幼虫在树干的垂直分布主要区间在50~150 cm之间。对幼虫垂直分布与树干高度的关系进行分析,其符合立方曲线,曲线方程为:Y=-5.142 9+17.943 7X+21.662 3X2-14.545X3;相关系数R2=0.915,P=0.013。     

林木分布格局多样性测度方法: 以阔叶红松林为例

林木分布格局是森林结构的重要组成部分, 直接影响森林生态系统的健康与稳定, 维持森林结构多样性被认为是保护生物多样性的最佳途径。本研究探讨了林木分布格局多样性的测度方法, 以期为揭示森林结构多样性提供理论依据。格局多样性研究的关键在于选择合适的生物多样性测度方法和具有分布属性的格局指数。本研究通过统计角尺度分布频率和Voronoi多边形边数分布频率, 运用Simpson指数分别计算角尺度多样性和Voronoi多边形边数分布多样性, 作为表达林木分布格局多样性指数的方法, 并以我国东北吉林蛟河的3个100 m × 100 m的阔叶红松(Pinus koreansis)林长期定位监测标准地为例, 分析了林木分布格局的多样性。结果表明: 无论是角尺度分布还是Voronoi多边形的边数分布都接近正态分布, 角尺度分布中随机分布林木的频数最多, 占55%以上; Voronoi多边形的类型多达10个以上, 50%以上的林木有5-6株最近相邻木。利用Simpson指数衡量林木格局多样性, 角尺度分布与Voronoi多边形的边数分布都显示出聚集分布的林分比随机分布林分的格局多样性高。研究还发现, 两种格局判定方法得出的Simpson指数值有所不同, 角尺度分布的多样性数值明显低于Voronoi多边形的边数分布的多样性数值, 主要原因是二者的等级数量不同。可见, 林木分布格局多样性研究应选择具有分布属性的格局指数, 但由于各指数反映的角度不同, 所以在分析比较不同林分格局多样性时应采用相同的分析方法。     

长白松自然同龄种群分布格局的研究

以长白松（Ｐｉｎｕｓｓｙｌｖｅｓｔｒｉｆｏｒｍｉｓ）种群为例,通过种群发展历史、种群大小结构研究,发现种群的胸径服从正态分布Ｎ（１６．８７,６．８０２）,确认该种群为自然同龄种群．种群的空间分布格局呈很高的均匀性,趋于随机分布甚至均匀分布,分布格局动态表现出由均匀分布向随机分布变化的趋势．     

中国蜡梅属种质资源的分布及其特点

根据对中国蜡梅属种质资源的调查,结合已有资料,重点阐述了中国蜡梅属植物的地理分布、水平和垂直分布特点及其生境特点。现知中国蜡梅属植物主要分布于我国的13个省,其水平分布很广,很连续,主要分布于秦岭以南、横断山脉以东的广大地区。垂直分布跨度很大,但垂直分布的上下限与经纬度无显著的相关性。蜡梅属植物对水热条件要求较严格,土壤基质多为沙壤土,在群系组成中,蜡梅属植物多为林木层和灌木层的优势成分。蜡梅属植物跨有5个植被类型,主要生长在常绿落叶阔叶混交林和常绿阔叶林地带。     

椭圆分布函数模拟水稻冠层叶倾角分布

利用双参数椭圆分布函数,结合Powell法寻优,对水稻冠层叶倾角分布进行模拟,并与实测值进行比较,取得了较为满意的结果。     

吉林蛟河阔叶红松林物种多度分布模型研究

以吉林蛟河阔叶红松林的木本植物为研究对象,将30hm²的样地面积划分为5m×5m,10m×10m,20m×20m,25m×25m的连续取样单元,在4个不同尺度下分别统计各物种在每个取样单元中的有无,得到每个物种在不同尺度下的取样单元数。利用随机分布模型和负二项分布模型分析物种的多度分布,对比预测多度与观测多度讨论两个模型的科学性与实用性。结果表明：对于阔叶红松林而言,负二项分布模型在所有研究尺度上的预测精度都要优于随机分布模型。随机分布和负二项分布的模型预测误差随着研究尺度的增大而增大,因此选取较小的取样单元可以切实提高物种多度的预测精度。利用随机分布和负二项分布模型对多度较小的物种进行预测的效果要优于多度较大的物种。负二项分布模型适合用来模拟阔叶红松林的物种多度分布格局,并且模型的拟合效果受取样单元大小影响。     

麻城黄山松天然林直径分布

为研究黄山松天然次生林直径分布特征,以麻城市黄山松天然次生林为研究对象,采用标准样地调查,计算林分直径的偏度、峰度,林分直径分布的Shannon-Weiner和Simpson指数,运用负指数分布、normal分布、lognormal分布、logistic分布和Weibull分布等5种概率密度函数对黄山松天然次生林林分直...     

Bimodal Epidemic Size Distributions for Near-Critical SIR with Vaccination

We introduce a recursive algorithm which enables the computation of the distribution of epidemic size in a stochastic SIR model for very large population sizes. In the important parameter region where the model is just slightly supercritical, the distribution of epidemic size is decidedly bimodal. We find close agreement between the distribution for large populations and the limiting case where the distribution is that of the time a Brownian motion hits a quadratic curve. The model includes the possibility of vaccination during the epidemic. The effects of the parameters, including vaccination level, on the form of the epidemic size distribution are explored.     

空间分布型的形成过程研究

具合影个研究了广义空间分布型和复合空间分布型的形成问题,解释了空间分布型的形成机理,并给出了１１种广义空间分布型和９种复事空间分布型;同时提出了空间分布型的３种判定方法：扩散系数法、空间相关法和参数变动法,它们以可用于区分常见的空间分布型,也可以用于判定分布型的形成过程;为研究空间分布型的形成机理和变化规模提供了有力的手段。以马尾松毛虫的空间分布型的研究结果表明,马尾松毛虫幼虫的空间分布型是复合负     

白花油麻藤的地理分布及适生区预测

白花油麻藤是豆科黧豆属大型木质藤本植物。运用Diva-Gis软件,结合海拔高度图层和植被图层绘制了白花油麻藤的地理分布图,分析了白花油麻藤的分布规律和生境特性;以Maxent模型作为物种适生性预测模型,温度和降水作为预测的环境因子,预测了白花油麻藤在中国的适生区。结果表明:白花油麻藤在中国27.5°N以南中低海拔10～1200m有分布,如山坡、路旁、沟谷、溪边及林下灌丛;喜温暖湿润气候,广东为白花油麻藤分布最为密集的地区。白花油麻藤的分布与植被类型和海拔有着密切的关系,分布区的植被类型为亚热带常绿阔叶林和热带季雨林,随着植被分布密度的降低和海拔的升高白花油麻藤的分布范围和分布密度呈逐渐缩小的趋势。白花油麻藤在中国的潜在分布区为粤、桂、闽、港、澳、滇、琼、赣、川、黔、藏、湘、浙等省区及交界处,其种质资源的保存及其利用应考虑其潜在分布区。     

Boltzmann-type distribution of side-chain conformation in proteins

We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C-C and C-S torsion angles (chi(3)) correlates well with the Boltzmann factor of the torsion energy, exp(-betaE) of the model compounds C(2)H(5)-C(2)H(5) and C(2)H(5)-S-CH(3). An exponential relation was again found between the relative occurrence of g+, g- and t conformations for C(alpha)-C(beta) bonds in long side chains and the energy differences of rotamers of alpha-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model's rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the beta-conformation, but less clear for backbone alpha-conformation. In all correlations, the value of the coefficient beta corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium.     

Do small animals have a biogeography?

It has been stated that small organisms do not have barriers for distribution and will not show biogeographic discreteness. General models for size-mediated biogeographies establish a transition region between ubiquitous dispersal and restricted biogeography at about 1–10 mm. We tested patterns of distribution versus size with water mites, a group of freshwater organisms with sizes between 300 μm and 10 mm.We compiled a list of all known water mite species for Sierra del Guadarrama (a mountain range in the centre of the Iberian Peninsula) from different authors and our own studies in the area. Recorded habitats include lotic, lentic and interstitial environments. Species body size and world distribution were drawn from our work and published specialized taxonomic literature. The null hypothesis was that distribution is size-independent. The relationship between distribution and size was approached via analysis of variance and between size and habitat via logistic regression. Contrary to expectations, there is no special relationship between water mite size and area size distribution. On the other hand, water mite size is differentially distributed among habitats, although this ecological sorting is very weak. Larger water mites are more common in lentic habitats and smaller water mites in lotic habitats. Size-dependent distribution in which small organisms tend to be cosmopolitan breaks down when the particular biology comes into play. Water mites do not fit a previously proposed size-dependent biogeographical distribution, and are in accordance with similar data published on Tardigrada, Rotifera, Gastrotricha and the like.     

白冠长尾雉(Syrmaticus reevesii)在贵州的分布与数量

白冠长尾雉(Syrmaticus reevesii)是我国的珍禽,分布于河北北部和西部、山西、陕西南部、湖北、湖南西北、贵州北部、河南西部、安徽西部及四川东部(郑作新,1978);还发现于甘肃南部的康县(刘乃发,1982)。1974—1982年,在贵州鸟类区系调查时,对于白冠长尾雉的分布、生态及数量曾作过初步研究,复于1983—1985年间,对它的生态生物学进行专门研究。本文仅就它在贵州省的分布和数量予以报道。