To elaborate:
If
X = (convolution of p(a), q(a) ,r(a))/(convolution of p(a), q(a))
Y = (convolution of p(a), q(a) ,s(a))/(convolution of p(a), q(a))
Why is X almost equal to Y even if (convolution of p(a), q(a) ,r(a))> (convolution of p(a), q(a) ,s(a))?
I'm unable to comprehend what happens. Please help. Thanks.
Hi,
1) I am not sure what you mean by the sign > between two functions of the variable a.
2) There is always a loss of information in convolution but the relative value of X and Y should stay the same as the one between convolution(p,q,r) and convolution (p,q,s) as you divide by the same value convolution(p,q).
Are you sure:
- there is no error
- convolution(p,q) is not 0 or near machine precision
- convolution(p,q) is not infinite, too high or near machine maximum
Jacques
Thank you for your answer.
By " > ", I meant one is greater than the other.
I'm sure there's no error, it's not 0 or infinite.
For eg. 756/15 and 740/15, both of which are approximately 50.
My point is the difference between the convoluted functions in the numerator (which is observed graphically) gets lost in the final number - which is kind of not doing justice to the difference observed in the plots of just the numerators.
Hi,
My point was that "greater than" cannot be mathematically defined between two functions. One function can have values greater than the other for some values of the variable and lower for some other values of the variable.
Are you certain that the denominator is not large for values of the variable where the difference between the numerators is large, which would tend to lower the difference between X and Y.
Could you plot both numerators and the denominator?
Jacques
Thank you very much for clarifying so many things Jacques B Sombrin .
"Are you certain that the denominator is not large for values of the variable where the difference between the numerators is large, which would tend to lower the difference between X and Y. "
Yes this is exactly how it is: The denominator is large for values where the difference between the numerators is large.
I'll share the plots via messaging shortly.
As a follow up question: Does it mean that the difference observed for the plots of the numerators is not a valid difference?
The absolute difference is valid but the division by the denominator introduces a weighting that may be important to consider in some cases.
Remark that the relative difference (Y-X) / X stay the same as
[ convolution(p,q,s) - convolution (p,q,r) ] / convolution (p,q,r)
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