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I have the following expression which I want to normalize:

val = v1+ v2
v1: has real values >0
v2: has values between 0 and 1

I want to normalize val such that it gives values between 0 and 1.

Best regards,

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    What are v1 and v2, random variables ? – 2017-01-14
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    @callculus they are real numbers – 2017-01-14
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    It quite depends on what you want to preserve. Per se, you could pick $\frac2\pi\arctan val$, or $\frac{val}{1+val}$. – 2017-01-14
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    Your problem has nothing to do with random variables ? I don´t get your problem. – 2017-01-14
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    My problem does not have anything to do with random variables, I just want to have an approach that could normalize val by returning values between 0 and 1. I think that what suggested @G. Sassatelli could solve the issue. I do not know if there are other possibilities. – 2017-01-14

1 Answers 1

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Given your definition:

val = v1+ v2
v1: has real values >0
v2: has values between 0 and 1

we know that val is a real value $>0$. Mapping this onto a value between $0$ and $1$ simply requires a monotonic function that stays small as its input goes to infinity. A simple option might be $\text{val}_{\text{norm}} = 1-2^{-\text{val}}$

If you wanted more weight on v2 in the result you might consider normalizing v1 instead and then adding & scaling into the desired range.