作者einstein328 (pica)
看板Statistics
标题Re: [问题] central limit theorem
时间Wed Oct 11 01:57:19 2006
底下是我找到的演算法 (参考於
http://www.dspguru.com/howto/tech/wgn.htm)
The Central Limit Theorm states that the sum of N randoms will approach normal distribution as N approaches infinity.
We can outline an algorithm that uses this approach as:
X=0
for i = 1 to N
U = uniform()
X = X + U
end
/* for uniform randoms in [0,1], mu = 0.5 and var = 1/12 */
/* adjust X so mu = 0 and var = 1 */
X = X - N/2 /* set mean to 0 */
X = X * sqrt(12 / N) /* adjust variance to 1 */
=============================================================
Q1:在统计上，uniform 跟 normal 有什麽差别吗?(因为 大大提到，用
rand()所产生出来的随机值除32767，会得到uniform的随机值(值介於0~1)
固有此一问)
Q2:刚刚大大提到，若是将所有取样做平均，即可得到具有 normal特性的随机值
可是上面的演算法中，只有把取样加起来而已，那?
撷取如下 :
X=0
for i = 1 to N
U = uniform()
X = X + U
end
Q3:那关於如何改变随机值中 normal的特性，演算法中也有提到
，我不了解他为什麽可以这样做?
截取如下 :
X = X - N/2 /* set mean to 0 */
X = X * sqrt(12 / N) /* adjust variance to 1 */
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