On Wed, Jan 18, 2017 at 4:30 PM, <josef.p...@gmail.com> wrote: > > > Having more sampling schemes would be useful, but it's not possible to >> implement sampling schemes with impossible properties. >> >> > > BTW: sampling 3 out of 3 without replacement is even worse > > No matter what sampling scheme and what selection probabilities we use, we > always have every element with probability 1 in the sample. >
I agree. The random-sample function of the type I envisioned will be able to reproduce the desired probabilities in some cases (like the example I gave) but not in others. Because doing this correctly involves a set of n linear equations in comb(n,k) variables, it can have no solution, or many solutions, depending on the n and k, and the desired probabilities. A function of this sort could return an error if it can't achieve the desired probabilities. But in many cases (the 0.2, 0.4, 0.4 example I gave was just something random I tried) there will be a way to achieve exactly the desired distribution. I guess I'll need to write this new function myself :-) Because my use case definitely requires that the output of the random items produced matches the required probabilities (when possible). Thanks, Nadav.
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