F分布和χ~2分布之间的渐近关系与性质

The Asymptotical Properties between Distribution and Distribution

我们分别基于F分布和X2分布的密度函数和随机变量的大样本性质证明了YLX/n(m→∞),其中Y服从自由度为(n,m)的F分布,X服从自由度为n的2χ分布;并进一步阐述了两者之间的渐近性质.我们通过模拟绘图以及分别计算密度函数、分布函数的误差绝对值和来进一步证实我们的结论。

In this paper, the conclusion Y→^L X/n（m→∞）, that follows distribution with freedom degree and follows distribution with freedom degree , is proved in two ways. One is by density functions, and the other by large sample properties of random variables. Also, some properties of this asymptotical relation are expatiated. Finally, our conclusions are further confirmed by picturing the density functions and computing respectively the absolute errors of the two density functions and cumulative functions.