Can you tell me any ways to generate non-uniform random numbers?
I am using Java but the code examples can be in whatever you want.
One way is to create a skewed distribution by adding two uniform random numbers together (i.e. rolling 2 dice).
What distribution of deviates do you want?
Here is a technique which always works, but isn't always the most efficient. The cumulative distrubtion function P(x) gives the fraction of the time that values fall below x. Thus P(x)=0 at the lowest possible value of x and P(x)=1 at the highest possible value of x. Every distribution has a unique CDF, which encodes all the properties of the distrubtion in the way that P(x) rises from 0 to 1. If y is a uniform deviate on the interval [0,1], then x satisfying P(x)=y will be disributed according to your distribution. To make this work comuptationally, you just need a way computing the inverse of P(x) for your distribution.
The Meta.Numerics library defines a large number of commonly used distrubtions (e.g. normal, lognormal, exponential, chi squared, etc.) and has functions for computing the CDF (Distribution.LeftProbability) and the inverse CDF (Distribution.InverseLeftProbability) of each.
For specialized techniques that are fast for particular distrubtions, e.g. the Box-Muller technique for normaly distributed deviates, see the book Numerical Recipies.
Try generating uniformly distributed random numbers, then applying your inverted non-uniform cumulative distribution function to each of them.
If you are using Java then my Uncommons Maths library may be of interest. It includes classes for generating random numbers for Uniform, Gaussian, Poisson, Binomial and Exponential distributions. This article shows how you might use these distributions.
来源：https://stackoverflow.com/questions/977354/generating-non-uniform-random-numbers