On Tue, 6 Nov 2007, Mike Hill wrote:
int choose( int range, int degree-of-randomness)
Returns an integer in [0-range] distributed depending on the value of
degree-of-randomness. At degree-of-randomness 100, I want the distribution
to be uniform. At degree-of-randomness 0, I want the distribution to be --
I don't even know what to call this -- half-of-a-normal-distribution with
the steepness proportionately related to degree-of-randomness.
This seems not so much the degree of randomness as the skew. Because a
normal distribution has an infinite continuous range, I don't think that's
what you want. You say "half a normal"; is something like a geometric
distribution close enough? You might check it out, at least it's
discrete.
But when I have a problem like this, I tend to use what I think of as the
"weight, bisect" algorithm. See if this solves your problem. Basically,
skew can go from 0 to infinity, and the higher it is, the steeper the skew
and the less likely you are to choose 0, the more likely you are to choose
size-1.
[begin python code]
from bisect import bisect
from random import random
def draw(weights):
sigma = 0.0
ps = []
for p in weights:
sigma += p
ps.append(sigma)
return (ps,random()*sigma)
def choose(size, skew):
'''
skew=0 gives uniform distribution
skew=1 gives linear, skew = 2 quadratic, and so on.
'''
weights = [i**skew for i in range(size)]
return draw(weights)
[end python code]
HTH,
Tom
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