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Random sampling from a discrete interval is relatively simple. Here my code is Python, but also straightforward in R and others.

position = random.randint(1, 100)

I would like to introduce a small bias in the sampling so that it's slightly more likely to draw from the range [75, 100]. My naive first attempt was as follows.

position = random.randint(1, 100 + 25)
if position > 100:
    position -= 25

However this results in very elevated sampling at both ends of the interval. How would I 1) restrict the bias toward only one end of the interval; and 2) control the intensity of the bias?

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As the question was asked in terms of Python, I will answer in the same way:

You can use numpy.random.choice(), which allows you to specify arbitrary weighting, via the p parameter.

The only annoying thing is that it requires p to be a probability array with sum = 1, rather than allowing an arbitrary weight array with entries >= 0. (So I always end up making a normalize_sum command.)

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