Thread: December 2019
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Old 2019-12-06, 07:17   #10
axn
 
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Jun 2003

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Quote:
Originally Posted by LaurV View Post
However I do not understand this part about final division by 2, that you, uau, and b2 are talking about. Why should you divide the interval? The mean is for ALL the domain, not only for pieces of domain. That is the reason of it, if your interval is longer, your approximation should be for all the interval, not per unit of interval. Otherwise the MSE makes no sense. In this light, their example has a MSE of 0.33333, that's it.
You have to sum all the error squares (which is the integral) and take the average to get the mean, by dividing it by the length of the interval (1 - -1 = 2).

Here is a simulation to convince you:
Code:
myrand()=(random(2^64)-2^63)/2.^63; \\ random real number in the range -1..1
sum(n=1, 10^4, r=myrand(); e=abs(r)-(r+1)/2; e^2)/10^4
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