Generating Nonuniform Random Deviates
Probability theory says...
- ...given a probability distribution u(z)
- if x is a function x(z),
- then the distribution of p(x) obeys
Prescription for p(x)
- solve this equation for x(z)
- generate z from the uniform random generator
- compute x(z)
Example
- we want on x = (0,1)
- then
- so x = z1/2
- taking square root of uniform deviate gives linearly distributed values
Generating p(x) requires knowledge of
a and c from “boundary conditions”