对数分布

Fri particular, the Wittmann-type strong law of larg numbers for independent random variables is generalized to the case of NA random variables. We also present the sufficient and necessary condition of the laws of logarithm, and we extend Teicher-type strong law of the large numbers for sequence of NA random variables. Some of the laws of iterated logarithm of Teicher-type, Egorov-type arid Wittmann-type for sequence of NA random variables are obtained. Then we investigate the rate3f ionvergcll( fbr series of NA randonl variables, we obtain soIne results fbr tl1e Iaws of theiterated logarithttl, the laws of logarithm and decreasing order fOr the tail sum.Risk itllttlysis tlleory is a sigIlifica11t part of insurance InatheInatics.

Wittmann（1985a）关于实独立随机变量列的结果，并给出了NA列强大数律成立的若干条件，特别建立了一般NA列对数律成立的充分必要条件，在二阶矩存在的条件下完整的解决了一般NA列对数律的问题，中文摘要2而已有的一些NA列对数律的结果可以由它推出，给出了NA列的Teiclier型强大数律，表明lbiChCI·（1979）给出的实独立随机变量列的强大数律可以减弱其条件等；建立厂不问分布NA列的Teicfl仪；Egorov，Petrov型有界重对数律，以及加权同分布NA列的有界重对数律，进一步推广了NA列的Kolmogory有界重对数律等，特别对NA列建立了Wittm洲型有界重对数律，而其证明方法与独立情形有很大不同，同时通过反例表明在与独立场合类似的条件下，独立列的Wittmann有界重对数律不能完美的推广到NA歹小惰形；最后研究了NA随机变量级数的收敛速度，给出了尾和下降的阶；尾和的有界重对数律，及尾和对数律成立的充要条件等，并通过反例说明 NA随机变量级数与独立随机变量级数在收敛速度方面存在的差异。

The near bottom velocity profile deviates from traditional logarithmic distribution.

近底流速剖面偏离传统的对数分布。

Based on analysis and certification of a large number of measured data of different channels and different discharges, it is shown that weather theoretical form or measureds results of lateral velocity distribution are consistent with the laws of logarithmic distribution.

大量不同梯拱形渠道、不同流量的流速实测数据分析和验证表明，理论与实测流速横向分布都符合对数分布规律，利用多变量回归分析，确定了流速横向分布系数a、b值。

In the studies for Fe_3O_4 nano-particles, the Preisach distribution was the product of the interaction field and coercive filed distribution, and the interaction field distribution was logarithmic;the coercive filed distribution were Gaussian.

在对Fe_3O_4颗粒的研究中，矫顽场的分布采用对数分布，相互作用场的分布采用Gaussian分布形式，Preisach分布函数为二者的乘积。

So,lognormal distribution is not the well life distribution of thismaterial.

结果表明，通常采用的对数正态分布的理论失效率呈单峰型，与材料经验失效率的变化不相一致，因此对数正态分布不宜作为稀土钼铜合金球墨铸铁材料裂纹萌生寿命的概率分布。

The negative binomial distribution, gamma distribution, and log-normal distribution were chosen as error distributions according to log-linear regression of variance versus log-mean of CPUE.

根据鲐鱼单位捕捞努力量渔获量数据呈正偏，以及CPUE均值与方差在对数尺度下的线性关系，选择了负二项分布、伽马分布与对数正态分布作为误差分布。

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。

A 3D particle velocity measurement system was built upon calibration method of multi-layer regular grid and particle space coordinates determination method of iterative approaching developed in this paper.

对不同的粒径和不同的水流条件，颗粒纵向平均速度都符合对数分布规律，垂向和横向的平均速度属于随机波动的范围。

It is found that water velocity vertical distribution under ice-cover is influenced mainly by the relative size of channel roughness and ice-cover roughness, less by the water depth and not sensitive to the variation of Reynold number as well, which is relatively uniform in the flow core and deviates from the logarithmic law.

结果表明：冰盖下水流流速垂向分布主要受床面与冰盖粗糙度的相对大小影响，受水深影响较小，对雷诺数变化并不敏感；在流动核心部分分布较为均匀，并不遵循对数分布规律。

It has been suggested that RADs from different habitat types tend to follow different RAD models, such as the logseries or lognormal distribution.

研究一直认为，来自不同生境的RADs秩--丰盛度分布倾向于符合不同的模型，如对数序列分布或对数正态分布。

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。