精确采样二元高斯
SAMPLING EXACTLY FROM THE BINARY GAUSSIAN
沈静 1杜育松2
作者信息
- 1. 广东工贸职业技术学院,广州 510510
- 2. 中山大学计算机学院,广州 510006
- 折叠
摘要
Karney于2016年提出了一种针对标准正态分布的精确采样算法.本文给出一种针对标准差为√1/(2 ln 2)均值为0的正态分布的精确采样算法.这一种特殊的正态分布也被称为二元高斯分布,因为其相对概率密度函数可以由2-x2给出,这里x为任意实数在实际中,针对二元高斯分布的这一精确采样算法无需浮点运算,可以看成是Karney精确采样技术的一种推广.分析了该采样算法产生一个二元高斯样本平均需要的区间(0,1)上的均匀偏差数.数值实验也表明了该采样算法的有效性.对于大于1但小于自然常数e的任意有理数c,将精确采样二元高斯分布的思想推广到了精确采样标准差为√1/(2 ln c)均值为0的被称为"c元高斯分布"的一类正态分布上,并进行了类似的复杂性分析.
Abstract
In 2016,Karney proposed an exact sampling algorithm for the standard normal distri-bution.In this article,we present an exact sampling algorithm for the normal distribution of standard variance √1/(2 ln 2)and mean 0,which can be called the binary Gaussian distri-bution,as its relative probability density function is given by 2-x2 for x ∈ R.Our proposed algorithm requires no floating-point arithmetic in practice,and can be regarded as the pro-motion of Karney's exact sampling technique.We give an estimate of the expected number of uniform deviates over the range(0,1)used by this algorithm until outputting a sample value.Numerical experiments also demonstrate the effectiveness of the sampling algorithm.For any rational number c greater than 1 but less than Euler's number e,the idea of sampling exactly the binary Gaussian is generalized to a class of normal distributions of standard vari-ance √1/(2 ln c)and mean 0,called"c-ary Gaussian distributions",and a similar complexity analysis is presented.
关键词
随机数生成/拒绝采样/正态分布/离散高斯分布Key words
Random number generation/Rejection sampling/Normal distribution/Dis-crete Gaussian distribution引用本文复制引用
基金项目
广东省基础与应用基础研究重大项目(2019B030302008)
国家自然科学基金(61972431)
广东省基础与应用基础研究项目(2022A1515011512)
广东工贸职业技术学院校级科研项目(2021-ZK-17)
出版年
2024
NETL
NSTL
万方数据