近似P-范分布的渐近正态性及柯尔莫哥洛夫检验  

Asymptotic normality of approximate P-norm distributions and Kolmogorov testing

作　　者：胡宏昌 王佳琪 HU Hong-chang;WANG Jia-qi(College of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《湖北师范大学学报（自然科学版）》2021年第4期1-6,共6页Journal of Hubei Normal University：Natural Science

摘　　要：P-范分布可以近似地由正态分布和拉普拉斯分布,或者是正态分布和均匀分布的线性组合来表示。在此基础上,运用特征函数的方法得到了近似P-范分布的渐近正态分布。利用统计软件生成120个服从P-范分布的随机数,通过柯尔莫哥洛夫检验进行拟合检验,其结果说明了近似P-范分布能够很好地替代P-范分布。The P-norm distribution can be approximately shown by the linear combination of the normal distribution and the Laplace distribution,the normal distribution and the uniform distribution.On the basis of the result,we obtain the asymptotic normal distribution of approximate P-norm distributions.120 random numbers of P-norm distribution are generated by a statistical software.Kolmogorov testing is used to test the approximate P-norm distribution.The results show that the P-norm distribution can be replaced by the approximate P-norm distribution well.

关 键 词：近似P-范分布 特征函数 渐近正态分布 柯尔莫哥洛夫检验 

分 类 号：O212.7[理学—概率论与数理统计]