中文摘要：

首先给出用[0,1]区间上均匀分布随机数产生的已知分布随机数生成定理,它是规则平面区域上均匀分布随机点生成的理论基础。其次,分别建立了矩形和椭圆区域内均匀分布随机点生成的定理,并且利用二维随机向量的联合分布与边缘分布的关系分别证明这2个定理。并以此为依据通过变换公式法分别提出了矩形和椭圆区域内均匀分布随机点生成的新算法,此算法产生无线网络的仿真系统中随机节点。

英文摘要：

Firstly,this paper gives the theorem to generate a given distribution random number by using uniform distribution random numbers in region.This theorem serves as the theoretical foundation to generate stochastic points in regular plane regions.Secondly,it presents the related theorems to generate the uniform distribution stochastic points in rectangular and elliptic regions and proves the two theorems by using the relationship between united distribution and marginal distribution of two dimensional random vectors,respectively.The nodes in the simulation system of wireless networks are generated by the new algorithm.