Question

How would you implement a function that is returning a random number from interval 1..1000
in the case there is a number N determining the chance of reaching higher numbers or lower numbers?

It should behave as follows:
e.g.

• if N = 0 and we will generate many times the random number we will get a certain equilibrium (every number from interval 1..1000 has equal chance).
• if N = 2321 (I call it positive factor) it will be very hard to achieve small number (often will be generated numbers > 900, sometimes numbers near 500 and rarely numbers < 100). The highest the positive factor the highest probability for high numbers
• if N = -2321 (negative factor) this will be the opposite of positive factor

It’s clear that the generated numbers will create for given N certain characteristic curve. Could you advise me how to achieve this goal and what curves can I create? What possibilities do I have here? How would you limit positive and negative factors etc.

thank you for help

Answer 1

If you generate a uniform random number, and then raise it to a power > 1, it will get smaller, but stay in the range [0, 1]. If you raise it to a power greater than 0 but less than 1, it will get larger, but stay in the range [0, 1].

So you can use the exponent to pick a power when generating your random numbers.

def biased_random(scale, bias):
  return random.random() ** bias * scale

sum(biased_random(1000, 2.5) for x in range(100)) / 100
  291.59652962214676  # average less than 500

max(biased_random(1000, 2.5) for x in range(100))
  963.81166161355998  # but still occasionally generates large numbers

sum(biased_random(1000, .3) for x in range(100)) / 100
  813.90199860117821   # average > 500

min(biased_random(1000, .3) for x in range(100))
  265.25040459294883   # but still occasionally generates small numbers