Any randomly generated numbers according to *non-uniform* probability distribution?

[William S. Shu]

I would like to attribute the probablity of events occuring based on known
(or user-defined probability distributions other than "uniformly random".
E.g.,  An agent has different probabilities of being in one of a number of
distinct positions, and has to visit it based on this probability.  The way
I currently implement it is associate each position with an interval of the
real line (in the range [0,1]), the length of which corresponds to its
probablility of being visited.  I then randomly generate numbers in [0,1].
If the number falls in the line segment corresponing to a position, I move
to that position.

The trouble is that I have a number of such scenarios, for different
situations with different probabilities.  I cannot easily build them,
especially for more complicated cases.

Do packages exist to do this, or similar?

In practical terms, could someone tell me if there are any random number
generators whose output over an interval [a,b] is generated with a
probability distributed according to common (known) or user-defined
probability distributions.  (Common distributions would include, say,
normal, binomial, distributions).  As a (crude) illustration, suppose such a
generator is producing numbers over the interval [-1.0,1.0] according to a
Normal Probability Distribution.  Then, it will produce any number in the
range [-1.0,0.0] with a probability of 0.5.

Thanks

William.



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