Mixture of Distributions
You can split the initial distribution into several simpler distributions:

In this case, random numbers for each of the distributions F
i
(x) are easy to generate. An appropriate algorithm may be as follows:
- Generate a random numberiwith the probabilityp.i
- Generate a random numbery(independent ofi) with the distributionF(ix).
- Acceptyas a random numberxwith the distributionF(x).
This technique is common in the acceptance/rejection method, when for the whole range of acceptable
x
values a density
g(x)
, which would approximate function
f(x)
well enough, is hard to find. In this case, the range is divided into sections so that
g(x)
looks relatively simple in each of the sub-ranges.
Since quasi-random sequences are non-random, you should be careful when using quasi-random basic generators with the mixture methods.