概率分布

To summarize two-dimensional non-normal joint distribution in use, such as Bivariate Weibull Distribution, Bivariate Log-normal Distribution, Bivariate Gumbel Distribution, and Bivariate Gamma Distribution.

归纳总结了已经出现的非正态二维联合概率分布模型，如二维威布尔分布、二维对数正态分布、二维冈贝尔分布及二维伽玛分布等。

In this paper, a speckle reduction method for SAR images based on Dual Tree Complex Wavelet Transform is proposed. It first presumes the probability distribution function for complex wavelet coefficients of the original nature image, and then applies MAP theory to estimate coefficients from the noisy wavelet coefficients. Filtered image can be derived after inversed DTCWT.

该方法首先对无噪声污染图像的复数小波系数的统计概率分布进行建模；然后利用此先验概率模型，采用最大后验概率方法从含噪小波系数中估计出无噪声污染的小波系数：最后经重构得到滤波后的图像。

The distribution function of the system response and state function is approximately determined by the standard normal distribution functions using Edgeworth series, and its reliability is obtained.

在结构系统响应和状态函数的前四阶矩的一般数学表达式的基础上，使用 Edgeworth级数把未知响应和状态函数的概率分布展开成标准的正态分布表达式，并放松了对随机参数的分布概型和激励类型的限制，从而确定了系统的可靠度

The final conclusion is that the demand distribution of currency is a exponential type distribution.

并分析了客户对银行货币需求的概率分布，将其归结为一个泛函极值问题，并进行了求解，结论是客户对银行货币需求的分布为指数分布。

The following conclusions have been made in this paper.(1) Based on CO_2 flux data of eddy covariance, variation characteristics of gross primary productivity in four flux observation stations were studied, which are an alpine meadow, an alpine shrub meadow, a swamp alpine meadow and a steppe alpine meadow at Dongxiong. The results show that photosynthetic capacity of the alpine meadow is the highest, and the annual total GPP is 652.2g C/m~2. Daily-differencing approach is used to analyze the random error of CO_2 fluxes measurements. The results show that the distribution of random error follows more closely follows a double-exponential, rather than a normal distribution, capturing the high peak and thick tail, and the random error varies with environment variables, which violates the assumptions for the ordinary least squares fitting with normality and homoscedasticity, consequently, we introduce maximum likelihood method for parameter optimization.

本文主要在以下几个方面开展工作并获得了一些认知和结论：(1)通过分析样带区域内高寒草甸、高寒灌丛、沼泽化湿地和草原化高寒草甸四个通量观测站点草地生态系统总初级生产力变化特征，研究结果表明HBBT矮嵩草草甸生态系统植被光合作用能力较强，年GPP总量为652.2 gC/m~2，明显高于其他三种生态系统；通过利用"单塔日变化法"获得四站点通量观测数据随机误差，结果表明通量观测随机误差概率分布呈现尖峰厚尾的特征，与正态分布相比，更服从双边指数分布，进一步分析表明通量观测随机误差随环境变量(风速、温度和光合有效辐射)的变化而变化，这违背了普通最小二乘法进行生态过程模型参数优化正态分布且误差同质的假设，因此本研究中引入最大似然法进行生态过程模型参数优化。

By summarizing the distribution of average speed on different types of road and the statistical distribution rule,it is concluded that the distribution of average bus speed in Beijing follows the law of logarithmic normal distribution.

对北京市公共汽车平均车速的在不同类型道路上分布的情况和统计分布规律进行了总结，提出北京市公共汽车平均车速分布遵循对数正态概率分布规律。

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。

We obtain the risk process involved in this model,the statistical properties of the surplus process,and statistical features of the claim numbers and the probability distribution of the total amount of compensation.The three types of business of the risk model is given when the number of claims obey Poisson distribution and negative binomial distribution.We make a comparison between the risk model built in the thesis and the classic risk models with independent claim numbers when the amount of claims obey Weillbull distribution and Exponential distribution.The results have a good practical significance.

其次，考虑不同险种间的相互关系，建立了一种含有主副理赔的风险分析模型；借助随机过程和经典风险理论，对该风险模型所涉及的风险过程、盈余过程的统计特性以及理赔总额的概率分布、数字特征和矩母函数进行解析研究，给出了主理赔次数服从泊松分布和负二项分布的这种风险模型的具体实例，并在理赔额变量服从Weillbul分布和Exponential分布的情况下，把文中所建风险模型和理赔次数相互独立的风险模型作了比较，所得结果有很好的现实意义。

A general model of two phase image segmentation based on variational level set method is proposed,and the region model is based on the image general probability distribution function.

基于变分水平集方法建立了两相图像分割的通用模型，其区域模型基于图像的一般概率分布函数，通过变分方法得到水平集函数的演化方程和符合常值分布、Gauss分布及Rayleigh分布的参数估计。

Based on the distance of Kullback-Leibler, this paper give the exact definition of the maximum Kullback-Leibler distance between two different distribution functions and prove that this one has analytic properties such as symmetry, triangle inequality which is the same as the Euclidean distance. By the definition, the maximum Kullback-Leibler distance between some conventional distributions, such as two different binomial distributions, two different normal distributions are obtianed.

在Kullback-Leibler距离的基础上，定义了两个概率分布之间的最大Kullback-Leibler距离，证明了这个距离具有欧式距离的对称性，三角不等式性等分析性质，依照该定义，计算了两个不同的二项分布，两个不同的正态分布等一些常见分布之问的最大Kullback-Leibler距离。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷