负二项分布

Through a probability problem,a connection is showed between binomial distribution and negative binomial distribution and therefore a composed formula is set up,which is proved by way of probability and algebra.

通过一个概率问题，给出二项分布与负二项分布的一种联系，从而建立一个组合公式，并由概率思维方式与代数方式给出证明

Therefore, in this article,we first discussed the compound negative binomial, it able to simultaneously fitthe claim size and the claim number. At the same time, we studied the sum of themutually independent compound negative binomial and the sum of the mutuallyindependent compound negative binomial with discount factor and the sum of themaximal compound negative binomial; Next, for the claim data to be better fitted, this article has establishedthe superposition distributed model about the weighted average of the discreterandom and has discussed the estimation method of the parameters of thesuperposition distribution; Once more, we in detail elaborated the NCD which based on the claim numberand the NCD which based on the claim size and the claim number. Besides, weestablished an applied NCD model which also based on the claim size and the claimnumber; At last, we introduced the rewards and punishment coefficient of automobiletravel region into the applied NCD model, availably consummated the present NCD.

因此，本文首先讨论了能拟合索赔额大小和索赔次数的复合负二项分布，并对相互独立的复合负二项分布的和、带有折现因子的相互独立的复合负二项分布的和以及最大复合负二项分布进行了研究；其次，为了更好地拟合索赔数据，本文建立了离散随机变量加权平均的叠加分布模型，并讨论了其中的权数的估计方法；再次，本文详细阐述了基于索赔次数的无赔款优待系统、考虑索赔次数和索赔额大小的无赔款优待系统以及应用型的同时考虑索赔次数和索赔大小的无赔款优待系统；最后，本文在无赔款优待系统中引入了汽车行驶区域奖惩系数，对现行的无赔款优待系统进行了完善。

Results: GLMMs allow the index may be one of the exponential family (Contimuum distributions including Nomal ,beta distribution ,chisquared distribution etc;Disperse distributions including Binomal ,Poisson and inverse Binomal etc), the vecor of expected means of the index is linked to the model parameters by a link function and model the linear equation, simple the calculator procedure.

结果： 广义线性混合效应模型允许临床疗效评价指标是指数家族中任意分布（如：连续分布包括正态分布、beta分布、卡方分布等；离散分布包括二项分布、泊松分布、负二项分布等），可以通过连接函数将疗效指标的均数向量与模型参数建立线性关系，简化运算过程。

Global maximum likelihood estimation was used to fit GNBD and negative binomial distribution. Results from different bottomlands in the same season and the same bottomlands in different seasons were compared with each other.

通过全局最大似然法分别拟合广义负二项分布和负二项分布，比较同一季节不同滩地和不同季节同一滩地的分布拟合结果。

Then,we improve CSFP Model in two aspects:when we ascertain the frequency of default,we use negative binomial distribution to substitute Poisson distribution so that the model can measure the data better;when we ascertain the loss distribution of default,we use Γ-distribution to substitute normal distribution.

其创新与特色一是对贷款组合的风险暴露数进行分段，在每一频段上分别确定风险暴露数分布，进而可以更准确的描述各笔贷款的风险暴露数。二是在确定风险暴露数分布时，用Γ分布替代了传统的正态分布，解决了贷款违约的风险暴露数分布的厚尾问题，进而解决了大宗贷款违约的风险度量问题。三是确定违约频率时，用负二项分布来代替传统的泊松分布，解决了违约频率的方差通常要大于其均值的分布拟合问题。

Generalized negative binomial distribution was successfully fitted to all the snail data. The parameters of GNBD from the same bottomlands in different seasons changed differently, and parameters of GNBD from different bottomlands in the same season were not similar even if their snail density were close.

不同季节同一滩地间的广义负二项分布参数的变化不一致，同一季节不同滩地广义负二项分布的参数估计结果即使在钉螺密度相近的情况下也不相近，钉螺生存环境的微小差异可以通过广义负二项分布的参数灵敏反映。

We studied its distribution pattem by using the following measures f the test for fitting to the poisson , negative binomial and neyman a distribution . at the same time , we use negative binomial parametef , dispersal index , patchiness index , cassie s index and clumping index , estimated the aggregation intensity . the results showed that the distribution pattern is typically aggregated , and the intensity of aggregation vari

经统计分析，青岛百合复合种群、各局部种群内个体的分布格局离散分布拟合的结果符合负二项分布；各聚集强度参数中，丛生指标）和 cassie 指标均大于o ，负h项参数限）均较小，扩散系数k卜扩散型指数）和聚块性指标均大于1 ，以上这些表明各个局部种群的分布格局都为聚集分布。

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。

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。

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。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。