7 ms·

So basically, your claim is that a normal distribution is less random than a uniform distribution? Can’t say I agree.

• deleted 3y ago
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• stavros 3y ago
  As I understand it, the claim is that the volume being added is tiny compared to the real volume.
• sillysaurusx 3y ago
  Well, by definition it is. It’s why we have names like normal and uniform.
  • uxp8u61q 3y ago
    By definition it's not. It's just as random. These names just tell you a few key properties of the distribution.
    • nomel 3y ago
      > just as random Let’s do a lottery together. We each throw in some money. Since they’re both just as random, I’m sure you won’t mind if I use a normal distribution, and choose each of our positions on the number line. :) Your assertion is missing some needed qualifiers.
    • maxbond 3y ago
      You've probably just got different understandings of the term "random."
    • jefftk 3y ago
      Would you say that a function that always returned 0 or 1 would be more/less/equally random than a function that returned any int32 with equal probability? I would normally say the latter is more random, because you're getting more entropy per call. In the same sense, a function drawing from a normal distribution is less random than one drawing from a uniform distribution. (All of this depends on a computers view of the world, where values are in data types that have some number of bits. In a mathy view of the world where every value is effectively infinitely many bits you get just as much entropy sampling from a normal distribution as a uniform one.)
      • eterm 3y ago
        > a function drawing from a normal distribution is less random than one drawing from a uniform distribution That's some mathematical nonsense. A normal distribution is continuous from negative infinity to positive infinity, so even by your flawed judgement of what makes something "random", a sample from the normal distrubtion has far more possibilities. The standard normal distribution is almost the definition of random.
        • jefftk 3y ago
          Again, it depends on whether you are looking at this from a pure math perspective or a "math as implemented on computers" perspective. I'm only claiming that this use of more/less random makes sense in a computational context. But in that context, there is more entropy in a float32 drawn from a uniform distribution than a float32 drawn from a normal distribution, no?
          • jefftk 3y ago
            Actually, I'm not sure this is mostly about a mathematical vs computational perspective. Let's look at how entropy is defined. It's not just the number of possibilities, it's how likely they are. For example, consider two functions: A: 1% chance of 1, 1% chance of 2, 98% chance of 3 B: 50% chance of 1, 50% chance of 2 The entropy of a distribution, in bits, is: H = - sum over all possibilities of (p * log_2 p) So for A it is: H_A = -(2 * 0.01 * log_2(0.01) + 0.98 * log_2(0.98)) = 0.16 And for B it is: H_B = -(2 * 0.5 * log_2(0.5)) = 1 So you can see that A has lower entropy than B, because it's more concentrated. For continuous distributions this is defined with an integral instead of a sum, but it's the same idea: H = - integral from -inf to + inf of (p * log_2 p) Whether there's more entropy in a sample drawn from a uniform or normal distribution, then, depends on how wide your distributions are. Consider: C: uniform distribution from -1000 to +1000 D: normal distribution centered on 0 with standard deviation 10 E: uniform distribution from -1 to 1 We then have: H_C = - log_2(2000) / log_2(2) = 10.97 H_D = 1/2 (log_2(2pi * 10^2) + 1) = 5.15 H_E = 1 Note that continuous and discrete entropies mean different things, and their values can't be compared directly. That H_E and H_B are both 1 is not meaningful.
    • sillysaurusx 3y ago
      That’s a bit like saying that our bodies are random numbers because of quantum fluctuations. It may be true, but the distribution is the part that matters. It’s still ridiculous to use a normal distribution to calculate how much money should go into an insurance fund that needs to cover sudden, severe losses.
  • sampo 3y ago
    > Well, by definition it is. If given only mean and standard deviation, the normal distribution is the maximum entropy distribution i.e. maximally random distribution.
• laurent_du 3y ago
  If you order randomness by entropy, the uniform distribution is indeed, in some sense, "more random" than any other probability distribution with the same support.
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