Recognitions:

## Random selection, with skewed distribution

 Quote by billiards Come up with an algorithm that picks out a random subset of those numbers, where the subset is biased towards the low numbers. Now I have an algorithm, but maybe someone has a better one? Surely someone has solved this kind of problem in the past!?
You haven't stated any criteria that can be used to judge whether one algorithm is better than another. Of course people have solved problems that this when they had well defined objectives. State what criteria makes one algorithm better than another and perhaps we can find the best method.

 This statement makes me suspect that you are not visualising the problem correctly
That could be true, but you haven't stated any well posed mathematical problem.
 I've taken a look at the code and there is absolutely no reason why you can't just define an appropriate multi-dimensional PDF that corresponds to your desired properties and then just use an MCMC type algorithm to draw independent random samples from that distribution.

 Quote by chiro I've taken a look at the code and there is absolutely no reason why you can't just define an appropriate multi-dimensional PDF that corresponds to your desired properties and then just use an MCMC type algorithm to draw independent random samples from that distribution.
Well there is one. I wouldn't know how to begin setting the thing up :(

 Quote by billiards Well there is one. I wouldn't know how to begin setting the thing up :(
Well ultimately the PDF has to have a probability that reflects the chance of something being picked.

You start off with a state space and then introduce constraints or assumptions to form your PDF.

The first thing is to define the scope of all possible atomic events that can happen. The second is to introduce the assumptions and extra constraints that narrow the PDF down to a specific form which will be used for sampling, and the next thing will be to use a technique like MCMC based pseudo-random algorithms that allow you to draw a pseudo-random sample from said distribution.

The thing about describing the state-space is that you will want to look at the largest atomic events that you are interested in and then define them mathematically. You can use all the set theory notation to define sub-sets and also the actual state space.

Once you do this mathematically, it will be much easier to go from that and then introduce some compact assumptions (like the probability is proportional to the inverse of the weight as discussed above) and then you will generate your PDF to sample from.

I'd recommend you do the above: define the state space first using the math terminology and then define the constraints and assumptions you use. Then take this and define the event of interest that corresponds to a single sample. Then from this you will get a better chance of getting a specific mathematical expression or at the very least, advice leading to that.

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