南京师大学报（自然科学版）Issue(3)：39-43,5.
卡方分布密度函数与分布函数的渐近展开
Asymptotic Expansions of the Probability Density Function and the Distribution Function of Chi-Square Distribution
摘要
Abstract
Through the transformation of the independent variable of χ2 distribution probability density function,degree of freedom of which is n,the equation can be expanded as follows: 2nχ2(x;n)=f(t;n)= 1+r1(t)n +r2(t)n +r3(t)n n +r4(t)n2éë ùûφ(t)+o 1n2( ) ,here,φ(t) is a density function of standard normal distribution;ri(t) is a 3i order polynomial of t(1≤i≤4). An approximate formula can be obtained from the expansion of the distribution density function. We further establish the integral recurrence relations of the power coefficients of the standard normal density function and obtain the asymptotic expansion of the distribution function ofχ2 . Finally,the effectiveness of these results in practical application was verified by the numerical calculations.关键词
χ2 分布/概率密度函数/分布函数/渐近展开/标准化变换Key words
χ2 distribution/probability density function/distribution function/asymptotic expansion/standard transforma-tion分类
数理科学引用本文复制引用
陈刚,王梦婕..卡方分布密度函数与分布函数的渐近展开[J].南京师大学报（自然科学版）,2014,(3):39-43,5.基金项目
江苏省自然科学基金(BK20141326)、江苏省高等教育教学改革研究课题重点项目(2011JSJG085) （BK20141326）
