Sunday, January 08, 2012


Non-Uniform Distribution from a Uniform Distribution

Given a uniformly distributed random variable x (such as the output from a standard Random Number Generator), how do we generate some other non-uniform distribution, q(y)?

Solution: Generate x, and take y = f(x). But how do we calculate f() given q() ?

The required function is the inverse cumulative distribution function given by:


Example: Exponential distribution (to simulate the lifetimes of radioactive nuclei)

clip_image003[4], (τ≥0,and = 0 otherwise)


So inverse is




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