Bell Curves

[Zaphod64831]

I've been struggling with a certain random number-related problem for a while. I need to be able to generate a random number from 0 to 100, weighting the 0 as most likely to occur and 100 least likely. When graphed it should look like half a bell curve, but the problem is that I don't quite know how to do it. I've tried reading up on bell curves, but I'm not exactly a great mathemetician.

The purpose of this random number generator is to decide upon a single monster in a large database of monsters which are given a rarity level of 0 for most common to 100 for extremely rare. Any help would be greatly appreciated.

[Acidic]

one way to do this (although might not be useful for trying to make a bell curve):
make an array called ints:
ints[0] = 1
ints[1] = 2
ints[2] = 3
ints[3] = 4
...
ints[99] = 100

Then another array called chance:
chance[0] = 30
chance[1] = 20
chance[2] = 15
chance[3] = 5
I think these should add up to 100, but I'm not sure if you have to make it do that.

then make another array called monster_array
make the first 30 items in it = 1.
then the next 20 items 2
the next 15 = 3
the next 5 = 4
etc.



Thinking about it, to get this to match a bell curve you have to plot a bell curve, note down the y co-ord for the first 100 positive integers then note down those integers into the chance array.

These will not add up to 100 but I don't think that matters.

[sql_lall]

It really depends what type you want:

You could have a binomial distribution - you start at 0, then you stop at that number with a probability of p, otherwise you go to the next number.
E.g. if you had p = 0.5, then you would have P(number = x) = 2^-x-1. This makes each number half as likely as the next.

OR There are other types of distributions though. You could have a normal distribution with mean zero, s.d. whatever you want, then just ignore all negative values (i.e. run again) and all those > 100 have as =100. This would be harder to code, yet possible. You'd have to account for continuity correction, P(number = x) = P(x - 0.5 < Stat < x + 0.5)

OR You could have linear degression. P(number = x) = k * p(number = x-1), where a suitable k is found such that the sum of probabilities is = 1.

OR You could use a cosine wave. Bit trickier, would have to multiply out so you have the sum of probabilities = 1, and spans 0 to 100. Still possible.