How do you generate random variables for normal distribution? - Answers

Random numbers (or deviates) can be generated for many distributions, including the Normal distribution. Programs like Excel include a function which will generate normal random variables. In Excel, you enter +norminv(+rand(),mean,stand dev). The formula can be copied down to generate many deviates. Hitting F9 will produce a new series. Be sure to enter a positive number for the standard deviation. Theory: Let X be a uniformly distributed random variable from 0 to 1. We want to generate deviates of distribution with a pdf of f(x) and a cumulative distribution of F(x) with F-1(x), the inverse CDF known. Generate a uniform deviate, a, and then calculate b = F-1(a) which will be distributed according to f(x). The related links are unfortunately quite mathematical. The problem with the normal distibution is that the inverse cumulative is not a simple equation, so table lookup is usually the fastest solution.