广义高斯分布随机变量生成算法

An Algorithm for Generalized Gaussian Random Variable Creation

以几个在［０，１］区间上相互独立的均匀分布随机变量为基础，综合运用了反函数法、变换抽样法、舍选抽样法以及综合法产生了广义高斯分布的随机变量，并给出了严格的理论证明以及详细的实现算法和实验结果。算法的推导和实现虽然是针对方差σ＝ １０，形状参数ｖ＝ ０．７ 的广义高斯分布完成的，然而通过相应参数的调整，该算法可以产生具有任意形状参数和任意方差的广义高斯分布随机变量。

Creation of random variable is the first step of data simulation experiments, for example, random variables of generalized Gaussian distribution are the basis of any theoretical research in the quantization coding algorithm of wavelet coefficients. The generalized Gaussian distribution, as the generalization of Laplacian and Gaussian distributions, is fixed by its standard deviation and shape parameter. Based on several independent uniformly distributed random variables over [0,1], a random variable of generalized Guassian distribution is created by combining inverse function method, transform sampling method, abandon selection sampling method as well as integration method. Theoretical proof is given and the detailed implementation and test results are also presented.