Discrete Inversion (Generating Random Sequences XII)


While this sounds something like a shameful family secret, discrete inversion is only the finite-valued variation on the method of inversion for the generation of random numbers with a given distribution (as I’ve discussed quite a while ago here). The case we’ll consider here is a random variable with few possible outcomes, each with different odds

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The Inversion Method (Generating Random Sequences IV)


In the first post of this series, I discussed how to generate permutations of sequences using the Fisher-Yates method and I explained (although indirectly) how a linear congruential generator works. In a second post, I explained how to generate 2D points uniformly and randomly distributed a triangle, discussing the method of rejection. In a third post, I’ve discussed how to generate points on a sphere.

All these methods have something in common: they are based on the uniform (pseudo)random generator, and they map uniform numbers onto a shape (or move numbers around, in the first case). What if we need another density function than uniform?

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