伪随机数随机性的一种新检验  

A new test on randomness of pseudo-random numbers

作　　者：时正华[1] 袁永生[1] 

机构地区：[1]河海大学理学院,江苏南京210098

出　　处：《河海大学学报（自然科学版）》2005年第2期232-236,共5页Journal of Hohai University(Natural Sciences)

基　　金：国家重点基础研究专项经费资助项目(G1999043604);水利部科技创新基金资助项目(SCX2001 20)

摘　　要：伪随机数通过的随机性检验越多,说明其随机性越好.利用生产的随机数精度固定这一特点,根据小数点后面n个数字之和,提出了尾数和的概念,并给出了求尾数和分布频数的算法.根据尾数和分布概率提出了一种检验伪随机数的新方法.当尾数较长时,尾数和的分布服从渐近正态分布.求出其期望和方差,并给出了求尾数和分布概率的近似估计公式.The more randomness tests the pseudo-random numbers pass, the better the randomness of the pseudo-random numbers. In consideration of the fact that the precision of random numbers produced is fixed, the concept of the sum of mantissa is proposed based on the sum of n numbers behind the decimal, and an algorithm for calculation of the distribution frequency of the sum of mantissa is developed. With the distribution probability of the sum of mantissa, a new method for testing the randomness of pseudo-random numbers is put forward. It is found that the distribution of the sum of mantissa is an approximately normal distribution if the mantissa is long. By derivation of the expectation and variance of the sum of mantissa, an approximate estimation formula for the distribution probability of the sum of mantissa is given.

关 键 词：伪随机数 随机性 检验 渐近正态分布 分布概率 估计公式 尾数 小数点 方差 期望 近似 

分 类 号：O242.1[理学—计算数学] O415.5[理学—数学]