Random distributions: normal vs. triangle

Discussion in 'Mod Development' started by ljfa, Dec 28, 2014.

  1. ljfa

    ljfa New Member

    Hi guys

    sometimes uniformly distributed random values such as generated by rand.nextDouble() don't cut it, one might want some values to be more common than others. Minecraft mostly uses uniform distributions, but sometimes it's not quite appropriate.
    One solution would be to add or subtract two independent uniform random numbers. This results in triangle distributed numbers.
    rand.nextDouble()-rand.nextDouble() gives a Triangle(-1, 0, 1) distributed value, with expected value 0 and variance 1/6. So they're fairly easy to compute.
    In nature many values instead follow a normal ("gaussian") distribution, e.g. sizes of livings, length of appendages, blood pressures.
    N(0, 1)-distributed values can be gotten from rand.nextGaussian(). This uses a slightly more complicated algorithm to create them from uniform distributed values.

    I'm currently using nextGaussian() for the size of flower patches and for the length of debuffs.
    How much does the triangle distribution differ from the normal distribution in practice? Would a player notice or care if one substitutes them? And how expensive is a call to nextGaussian()? Or are there other examples for distributions one could use?
    Or is it silly to even care about distributions at all?

    I'm currently learning stochastics and I'm kinda concerned about getting distribution, expected value and standard deviation right. That's why I ask.

    Here's a graph of the probability density for the normal, triangle and uniform distribution. In all three cases the expected value is 0 and the variance 1. Notice how much the uniform distribution differs from the other two.

    PS: To create triangle distributed values with expected value 0 and variance 1 you have to multiply rand.nextDouble()-rand.nextDouble() by sqrt(6).
    Last edited: Dec 28, 2014
  2. InfinityRaider

    InfinityRaider New Member

    I'd say a triangular distribution is a good approximation of the standard normal distribution, specifically for this application.
  3. ljfa

    ljfa New Member

    I wonder how impacting the limited range of the triangular distribution is. Very large values are (almost) impossible.
  4. InfinityRaider

    InfinityRaider New Member

    They are impossible yes, but the amount of times a significantly larger number from a Gauss curve (compared to the triangular) occurs negligible imo.
  5. ljfa

    ljfa New Member

    You're right. I should stop worrying about this :)
  6. InfinityRaider

    InfinityRaider New Member

    Why, it is quite an interesting matter, and that is just my opinion on it.
    ljfa likes this.

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