分布的

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。

Discrete and continuous random variables, theoretical distribution, expected value, binomial distribution and normal distribution, standardizing and normality.

间断性变数总体的理论分布重点掌握二项分布和泊松分布，连续性变数总体的理论分布重点掌握正态分布以及正态分布的标准化。

The results showed that the spatial distribution patterns of cochineal in cactus belonged to aggregation distribution, the basic component of distribution was individual population, the probability distribution was in accorded with negative binomial and the cochineal mainly distributed the second and third stem in cactus.

结果表明，该虫在寄主仙人掌茎片上的空间分布型属于聚集分布，分布的基本成分是个体群，概率分布符合负二项分布，主要分布在仙人掌的第2和第3级茎片上。

The main work can be summed up as follows: Firstly, we studied the thermal-field properties of VCSELs, and analyzed the influences of current spreading, material parameters and operating conditions on the temperature distributions. Secondly, we began with the electrode voltage and calculated the equipotential s distributions, compared the distributions of voltages and current densities in different depths of VCSELs, and then studied the influences of the oxide-confining region with different position or thickness, and the different sizes of the gain-guided aperture and emitting window on the distributions of the injected current density, carrier concentration and temperature in the active region. Thirdly, we realized the coupling of electricity, optical and thermal-fields, worked out the threshold voltage, calculated the distributions of the injected current density, carrier concentration and temperature under different offset voltages, and analyzed the impacts of temperature profile and carrier density on the refractive index, Fermi levels and optical-field. Finally, we gave the equipotential line distributions with considering N-DBR and double oxidized-confining regions, and analyzed theinfluences of N-DBR and double oxide-confining regions on the distributions of the current density, carrier concentration, temperature and optical-field.

具体工作可以概括如下：首先，研究了VCSEL的热场特性，分析了电流扩展，材料参数和工作条件对于温度分布的影响；其次，从电极电压入手，计算出激光器中的等势线分布，并对不同深度处的电压和电流分布进行比较，研究了高阻区的不同位置和不同厚度、限制层和出射窗口半径的大小对电流密度、载流子浓度和温度分布的影响；再次，实现了电、光、热耦合，求出了阈值电压，计算了不同偏置电压下的电流密度分布、载流子浓度分布和热场分布，分析了温度和载流子浓度变化对折射率、费米能级和光场的影响；最后，给出了考虑N-DBR和双氧化限制层时激光器中的等势线分布，分析了N-DBR和双氧化限制层对VCSEL电流密度、载流子浓度、温度和光场分布的影响。

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。

State of names 名字分布的情况 America's Social Security Service keeps a register that contains the 100 most popular names in each state every year and the number of babies given them.

美国的社会保障服务部存有一张登记表，包含每年每州最受欢迎的100个名字，以及取了这些名字的婴儿数量。

In this paper, a computer programme is discussed, which, as a mathema-tical model, can be used to calculate the probability distribution as respects random variable-normal, lognormal, binomial, negative binomial and Poisson distributions, and can be used for x2 test of goodness of fit as well.

本文是计算随机变量概率分布的数学模型—正态分布，对数正态分布、二项分布、负二项分布。普阿松分布及检验X~2适度检验的一个计算机程序。

Nowadays the researches of frequency distribution of data are almost limited to normal distribution, while other distributions are seldom studied. Many frequency distributions of data are not normal. This kinds of frequency distribution of data widely exist. Unimodal frequency distribution of data often occurs.

现在绝大多数关于频数资料分布的研究都是基于正态分布的，而对其他类型的分布研究得比较少，实际上频数分布在许多情况下并非呈现正态分布，分布的形态丰富多彩，很多资料都是呈现单峰分布，本研究就是利用数学上常见的八种连续型变量的分布类型去拟合单峰频数资料。

The 134 genera of vascular plants had 14 areal-types, including 42 cosmopolitans 55 temperate types 30 tropic types 2 Mediterranean-types, 2 East Asia types and 1 endemic species. The cosmopolitan and temperate type accounted for 31.34% and 41.04% of all the genera, respectively revealing the azonal feature of the wetland vegetations and the influences of cold and wet climate on the formation and distribution of the vegetations.

维管束植物属有14个地理分布区类型，包括世界分布属42属、温带分布属55属、热带分布属30属、古地中海属2属、东亚分布属4属、中国特有分布属1属，其中世界分布属和温带分布属分别占区系维管束植物总属数的比例较高，分别为31.34%和41.04%反映了湿地植被的隐域性和冷湿气候对湿地植被发育、分布的影响。

The partly cold-adaptation stratagem of the high altitude amphibian tadpole were researched in the laboratory by analyzing the high altitude amphibian tadpole of Scutiger boulengeri mainly on endpoints related to the dynamic variation of the micro-spatial behavior distribution patterns, the experiment of the temperature tolerance, and the enzyme content and activity of the lactic acid dehydrogenase isozyme in special temperature condition.The behavior distribution of the Scutiger boulengeri t...

西藏齿突蟾蝌蚪在不同温度的行为分布是一连续、动态过程，需用多种检验方法综合利用才能进行判断；在15℃，除低海拔分布的西藏齿突蟾种群外所有实验物种蝌蚪均符合负二项分布、NeymanⅡ型分布；在10℃，高海拔两栖类蝌蚪均符合负二项分布、NeymanⅡ型分布；在5℃、0℃低温时，高海拔两栖类不同分组的西藏齿突蟾蝌蚪的负二项分布、NeymanⅡ型分布均呈现明显差异，这可能与高海拔两栖类蝌蚪在低温条件下通过不断地改变其行为分布方式来避免自身被冻伤有关。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。