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Finishing calculation of mean value, standard deviation, skewness, kurtosis of Beta distribution.(2) Fitting parameters of many kinds of typical distribution and using residual deviation to evaluate fitting precision.(3) Using Beta distribution as an agreed indication distribution applied to many kinds of practical photoelectric measurement distributions.(4) Deriving theory formula of Bayes point estimation about Beta distribution parameters and mean value and standard deviation on the condition of mean square error loss function and supposed the prior distribution is uniform distribution.(5) Generating MCMC sample from post distribution by the method of Gibbs sample algorithm. Calculating bayes point estimation from sample on the condition of mean square error loss function. Calculating confidence interval by an approximate method to complete interval estimation.
本文的主要工作有：(1)解决了Beta分布参数a和b的精确计算以及均值、标准差、偏度、峰度的计算问题；(2)拟合出10余种典型分布的Beta分布的两个参数，并且采用剩余标准差评价该Beta分布的拟合精度；(3)对多种典型的光学与光电测量系统的测量分布进行了Beta分布统示表示；(4)在假设先验分布为均匀分布前提下，得到参数a和b以及均值μ和标准差σ在均方误差损失函数下的贝叶斯点估计理论计算公式；(5)利用直接抽样的Gibbs抽样算法，从后验分布中产生MCMC样本，从样本直接计算均方误差损失函数下的贝叶斯点估计，并使用一种近似方法计算其置信区间，完成区间估计。
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Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .
本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。
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The distributed pattern shows different between the probability distribution of water depth of rain gauge and that of soil moisture in horizontal section of different depth.
在毛乌素沙地，喷灌前后土壤含水率等值线垂直分布均具有显著的垂直分层特征；在喷灌结束24h后，喷灌前土壤含水率的垂直分布与喷灌后土壤含水率的垂直分布间地相关性较弱；灌水前土壤初始含水率的概率分布形态均表现为较典型的左偏态分布，灌后土壤含水率分布形态表现为左偏态、右偏形态或正态分布；雨量筒水深概率分布与土壤不同深度剖面层水平方向的含水率概率分布在形态特征上表现出一定程度的差异，雨量筒水深分布与水平层土壤含水率分布、灌后相邻深度层土壤含水率分布、之间的相关程度较高，其相关性随着剖面深度和层间距的增加而降低。
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In the Mu Us desert, either vertical distributions of soil moisture isogram before irrigation or vertical distributions of soil moisture isogram after irrigation shows obviously vertical-layered character. When the irrigation is finished 24 hours later, there is little correlation between vertical distributions of soil moisture isogram before irrigation and vertical distributions of soil moisture isogram after irrigation. All of probability distribution of soil water content before irrigation are left-skewed distribution, but some of probability distribution of soil water content after irrigation is left-skewed distribution, some is right-skewed distribution or normal distribution. The distributed pattern shows different between the probability distribution of water depth of rain gauge and that of soil moisture in horizontal section of different depth. There is close correlation between the distribution of water depth of rain gauge and that of soil moisture in horizontal section, but the correlation debases as the horizontal section turns deeper. Also after irrigation close correlation occurs between the distribution of soil moisture of layers bordering upon each other, but which reduces with space of different layers being larger.
在毛乌素沙地，喷灌前后土壤含水率等值线垂直分布均具有显著的垂直分层特征；在喷灌结束24h后，喷灌前土壤含水率的垂直分布与喷灌后土壤含水率的垂直分布间地相关性较弱；灌水前土壤初始含水率的概率分布形态均表现为较典型的左偏态分布，灌后土壤含水率分布形态表现为左偏态、右偏形态或正态分布；雨量筒水深概率分布与土壤不同深度剖面层水平方向的含水率概率分布在形态特征上表现出一定程度的差异，雨量筒水深分布与水平层土壤含水率分布、灌后相邻深度层土壤含水率分布、之间的相关程度较高，其相关性随着剖面深度和层间距的增加而降低。
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Climatic gradients were based on data sets from 841 meteorological stations throughout China. Definitions for floristic distributional patterns were based upon the work of Prof. Z. Y. Wu. Most of these floristic distributional patterns were strongly correlated with the geographic gradients in climate, except for cosmopolitan, cultivated and invasive genera. Tropical genera form a large fraction of the total genera (ranging from 0.84% to 94.38% in the regional floras) with the highest proportion in southern Yunnan and Hainan Island. Tropical genera occur predominantly in southern China of 0° N latitude and decreased with increasing latitude, as would be expected. Interestingly, the disjunct Tropical Asia and Tropical America distribution were not restricted to southern latitudes. Temperate genera account for 5.1% to 98.83% of the total genera in regional floras with the highest proportion in the province of Xinjiang. Most of these genera followed geographic gradients in climate as expected (temperate genera conspicuously dominate the landscape at higher latitudes), except the East Asian and North American disjunct distribution, Eastern Asian distribution and Chinese endemic distribution. Generally, most plant genera demonstrated some correlation with climatic and geographic gradients. The most important gradients were those of annual air temperature and precipitation. A small fraction did not demonstrate significantly particular pattern:"Cosmopolitan","East Asian and North American disjunct","Eastern Asian" and "Chinese endemic" distributions. The North Temperate distribution had the highest correlation with mean annual air temperature and precipitation.
结果如下：(1)除世界分布、栽培和入侵成分外，大部分中国种子植物属的地理成分的分布与地理相关密切；(2)热带分布属（泛热带分布、热带亚洲至热带美洲间断分布、旧世界热带分布、热带亚洲至热带大洋洲分布、热带亚洲至热带非洲分布及热带亚洲分布合计）占各地方植物区系的0.84%到94.38%，其最低值出现在中国西北部的新疆和青海地区，最高值出现在中国云南南部和海南；(3)热带分布属在＜北纬30°的地区占优势，除热带亚洲至热带美洲间断分布外，其它热带成分随纬度增加迅速减少；(4)温带分布属（北温带分布、东亚和北美间断分布、旧世界温带分布、温带亚洲分布、地中海区、西亚到中亚分布、中亚分布和东亚分布合计）占各地方植物区系的5.1%至98.83%，其最高值出现在中国西北部的新疆地区，最低值出现在中国云南南部和海南；(5)除东亚和北美间断分布、东亚分布和中国特有分布外，其它温带成分随纬度增加迅速增加；(6)在温带成分中，东亚和北美间断分布及东亚分布属主要出现在中国亚热带到暖温带地区，北温带分布、旧世界温带分布和温带亚洲分布属在中国北部占优势，而地中海区、西亚到中亚分布和中亚分布属则在中国西北部占优势；(7)除世界分布、东亚和北美间断分布、东亚分布和中国特有分布外，所有其他成分都显示了与气候因素密切相关，其中，北温带分布属与年均温和年降雨量最为密切相关。
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This thesis mainly discuss following issues, Theory and simple expressions for array covariance matrixes are derived when angular spread functions are symmetric distribution functions, i. e. the Uniform distribution, the Gauss distribution, the Laplace distribution and the Von Mises distribution, and a non-symmetric distribution function, i. e. the Gamma distribution. And the relation between the effective signal subspace and the array number, or and the nominal angle of the distributed source, the angular spread, the distributed functions, and the Signal-to-Noise Ratio is gained. The dimension of the effective signal subspace increases with increment of the array number. And it is more obvious to the non-symmetric distribution. The dimension of the effective signal subspace decreases with increment of the nominal angle. And the distributed source is equal to a point source as θ=π/2. The dimension of the effective signal subspace increases with increment of the angular spread.
本论文针对阵列信号处理中广泛存在的分布源现象，主要讨论了以下问题：推导了角度分布函数分别为对称的均匀分布、高斯分布、拉普拉斯分布、Von Mises分布和非对称的伽马分布时，分布源阵列接收信号协方差阵的严格模型和简化模型，得到了单个分布源的有效信号子空间随阵元数、分布源中心角、分布角、角度分布函数和信噪比的变化规律：随着阵元数的增加，对所有角度分布函数的有效信号子空间维数也随着增加，且非对称分布函数的有效信号子空间充满整个空间的可能性更大；随着分布源中心角逐步增加，有效信号子空间维数逐步减小，当θ=π/2时，等价于点源情形；随着分布源分布角逐渐加大，有效信号子空间维数也随之增加，直到有效信号子空间充满整个空间；随着信噪比的增加，有效信号子空间维数有一定程度的减少。
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In order to reduce calculation error, the frequency distribution of average values is used to compute the mixed distribution's digital features of each component distribution, thereinto, the number of the component distribution is determined by AIC, choose the number that meets the minimum value of AIC as the component number of mixed distribution, and the other parameters are estimated by EM algorithm; Secondly, because each component distribution is corresponding to a kind of major gene genotype, according to the values of the average and variance of the each component distribution, we can use the limit error of the normal distribution to plot each individual into the correspondent component distribution, namely into correspondent major gene genotype. Then we regard each major gene genotype as a treatment level of one-way analysis of variances, and the one-way multivariate analysis of variance is carried out to calculate the covariance matrix of major gene effect, covariance matrix of polygene effect, covariance matrix of environment effect and so on; At last, combining the weights of the each component distribution of mixed distribution, we can calculate the variance of major gene effect, the variance of polygene effect, environmental variance and the genetic gain of the quantitative trait.
为减小计算误差，本研究采用均值的频数分布来计算各成分分布的数字特征，其中成分分布个数根据AIC准则，选择使AIC值达到最小的成分分布个数作为混合分布的成分分布数，分布中其它参数的确定利用EM算法来估计；其次，每个成分分布对应一种主基因基因型，根据各个成分分布的均值和方差，利用正态分布的极限误差将每个个体划分到相应的成分分布中，即相应的主基因基因型中，将每种主基因型作为单因素方差分析的一个处理水平，对其进行单因素的多元方差分析，分别计算主基因效应协方差阵、多基因效应协方差阵、环境协方差阵等参数；最后结合混合分布中各成分分布的权重即各主基因基因型的分离比例，计算主基因效应方差，多基因效应方差和环境方差，以及遗传力等参数，进而计算该数量性状的遗传进展。
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I have calculated the species diversity for 3 layers (i.e. tree layer, shrub layer and herb layer) by means of various biodiversity index formulas and analyzed the relative species abundance using 9 models of the probability density distribution functions, such as, 3 Distribution (or Beta Distribution, Weibull Distribution, Lognormal Distribution, Poisson Distribution, Binomial Distribution, Negative Binomial Distribution ,Geometric Distribution, etc.. chi-square analyses were conducted on species distribution by using the chi-square test formulated by Pearson to test which distribution function is better, the result of chi square test made it possible to reject the other 8 distribution functions, theβdistribution function performs better than other probability density functions, it has a very close approximation, which can be used for the description of relative abundances of species in forest communities in this data set.
在相对多度研究上选用了九种概率分布模型，这九种概率密度分布函数依次为：贝塔分布、Weibull分布、对数正态分布、泊松分布、二项分布、负二项分布、几何分布、对数分布和奈曼A型分布，并进行了严格的卡方检验，结果表明：其它八种分布均被遭到拒绝，只有贝塔分布获得了通过，且拟合的结果非常理想。
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Asian (47.4%) and temperate genera mainly constituted by North temperate (50%) and E. Asian (50%). So that the geographical elements are discomplex. In the 25 species of arborous layer, 76% is the middle subtropical zonal type, 16% south subtropical zonal type and 8% north subtropical zonal type, of which the first 6 positions of important value index were all middle subtropical zonal type. This showed that the community was subtropical characteristic. There are 59.5% evergreen and 40.5% deblade of 79 known species in which the mid-phaenerophytes is the first position of all, accounting for 27.8%, and the evergreen broad-leaved species constituted the majority of meso-phaenerophytes which accounts for 15.2%.
乔木层多数优势种为稳定型种群，所以乔木层优势区系成分相当稳定，表明该群落为一种顶极群落。59个种子植物属只有10个分布区类型和4个变型，地理成分不复杂，其中热带分布27属占46.6%，温带分布31属占53.4%；热带分布以泛热带和热带亚洲分布为主，分别占52.6%和47.4%，温带分布为北温带和东亚分布各占50%。25个乔木层树种中，中亚热带地理分布类型的占76%，南亚热带地理分布类型的占16%，北亚热带地理分布类型占8%，重要值指数排列前6名的均为中亚热带地理分布类型，所以该群落为亚热带性质。
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In different conditions on fluidized state and stability of conical fluidized bed. The conlusions are: the conical angel of the conical fluidized bed is 20°, the fluidized state havesmall difference in conical distributor and distributor plate. The angle of conical bed increase,the fluidized state will have big difference. The angle is 60°and the conical as distributor, themass of fluidized is less, the most of material is the bottom of conical bed. The effect ofdistributor plate is much better than the conical distributor. Sawdust and rice hull can fluidize.The annular gap of conical distributor different, the angle of conical bed is same, the fluidizedquality of 10mm annular gap is better than the other conical distributors. The annular gap ismore wide, the conical bed have more slugging phenomenon and the pressure fluctuate is turnbig.In the experiment the flow of 2％and 4％distributor plates don\'t easy to control, becausethe pressure is very big and the pressure fluctuate of conical bed is too big.
在不同的条件下对锥形床的流化状态和稳定性进行了研究，结果得出：锥形床的锥角为20度时，分布锥和分布板的流化状态相差不明显，随着锥形床锥角的增大，分布锥和分布板的流化现象会出现明显的变化，锥形床锥角越大，分布锥的流化状态变化越明显，流化的的物料越少，大量物料都聚集在锥形床底部，而分布板在加料量少的情况下，能流化起来。10mm、15mm和20mm环隙分布锥在锥形床锥角相同条件下，10mm环隙分布锥的流化质量要好于其它两个分布锥，环隙越大越容易出现腾涌现象的产生，压降波动范围增大。2％、4％和6％开孔率分布板在本实验测定时，2％和4％开孔率分布板的流量不容易调节，同时产生的压降波动范围也很大，比较来说，6％开孔率分布板流化质量好些。
- 更多网络解释与分布相关的网络解释 [注：此内容来源于网络，仅供参考]
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Contagious Distribution：集群分布,蔓延分布 蔓延分布; 叢生分布
contagion 蔓延度 蔓延單位; 傳染 Y | contagious distribution 集群分布,蔓延分布 蔓延分布; 叢生分布 Y | contagious population 集群(分布)种群 蔓延族群 N
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distribution function：分布函数 分布函數
distribution fringe 分布周缘,分布边缘地区 分布周緣地域 Y | distribution function 分布函数 分布函數 Y | distribution of three phases 三相容积比 三相容積比 (土壤的) Y
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exponential：指數分布
这些作为零假设的理论分布在SPSS的选项中有正态分布(Normal),泊松分布(Poisson) ,均匀分布(Uniform)和指数分布(Exponential). 在SPSS软件中对于是否是正态分布或均匀分布的检验统计量为由于sig=.074>.05,不能拒绝正态分布(Normal)零假设.
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Poisson distribution：分布
Poisson分布(Poisson distribution)是一种离散分布. 常用于研究单位时间或单位空间内某罕见事件发生次数的分布. Poisson分布(Poisson distribution)是一种离散分布. 常用于研究单位时间或单位空间内某罕见事件发生次数的分布.
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probability distribution：概率分布
贝赛尔(Bessel)函数一、贝赛尔(Bessel)函数概率分布(probability distribution)是概率论的基本概念之一,用以表述随机变量取值的概率规律. 描述不同类型的随机变量有不同的概率分布形式,其中包括二项式分布、χ2 分布、F 分布、正态分布等.
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Sampling distribution of sample mean：样本平均值的抽样分布
sampling distribution 采样分布,取样分布,抽样分布,标本分布 | sampling distribution of sample mean 样本平均值的抽样分布 | sampling distribution of the statistic 统计量的抽样分布
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distribution-free sufficiency：分布不拘充分性;分布无关充分性
分布不拘法;分布无关法 distribution-free methods | 分布不拘充分性;分布无关充分性 distribution-free sufficiency | 分布不拘检定;分布无关检定 distribution-free tests
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altitudinal belt：海拔分布带,垂直分布带 垂直分布帶
altitudinal adaptation 海拔适应 海拔適應 Y | altitudinal belt 海拔分布带,垂直分布带 垂直分布帶 Y | altitudinal vicariad 垂直分布替代种,海拔高度替代种 垂直分布對應種 Y
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altitudinal vicariad：垂直分布替代种,海拔高度替代种 垂直分布對應種
altitudinal belt 海拔分布带,垂直分布带 垂直分布帶 Y | altitudinal vicariad 垂直分布替代种,海拔高度替代种 垂直分布對應種 Y | altitudinal zone 垂直分布带 垂直分布帶 Y
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adjacent-1 distribution;nonhomologous adjacent distribution;nondisjunctional distribution：邻接-1分布;非同型染色体邻接分布;不分离分布
"邻接分离","adj... | "邻接-1分布;非同型染色体邻接分布;不分离分布","adjacent-1 distribution;nonhomologous adjacent distribution;nondisjunctional distribution" | "邻接-2分布;非同型染色体邻接分布;不分离分...