作者binchung (ideal)
看板Statistics
标题Re: [问题] 分布收敛
时间Sun Oct 19 22:54:13 2008
Since {X_n}, {Y_n} are independent, (X_n,Y_n) converges to (X,Y) weakly
(it's obvious from the two dimensional characteristic function).
From the continuous mapping theorm (R^2->R^1), you can get X_n*Y_n converges
weakly to XY, where X and Y are random variables whose distribution are
F and G respectively.
※ 引述《wulingking (等的好辛苦)》之铭言：
: X_n,Y_n相互独立且c.d.f为F_n,G_n
: 又F_n,G_n分布收敛到F,G证F_nG_n分布收敛到FG
: 想法:因c.d.f.在0,1间...极限一定存在
: 故limF_nG_n=limF_n limG_n=FG
: 又觉得怪怪的@@
: 请问有问题吗
: 谢谢~
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◆ From: 76.124.84.13
1F：推 wulingking:感谢!虽然看不太懂@@ 10/19 23:34
2F：→ clickhere:上面有人回了,用chf,那就是continuous function. 10/20 03:33
3F：→ clickhere:所以在用这篇的continuous mapping thm就可以了. 10/20 03:33
4F：→ clickhere:原po, 再考资格考吗? 10/20 03:33
5F：→ knuk:他的ch.f是指特徵函数吧... 10/20 21:30