# How To Sample Random Numbers

1. Sep 5, 2005

### Watts

I had a Monte Carlo class many moons ago. I was wondering if some one could jog my memory on how to sample random numbers from a normal distribution. I could do it but the normal distributions CDF is a non elementary integral. I cant get past that part.

2. Sep 5, 2005

### EnumaElish

Let U1 and U2 be two independent uniforrm random variables over the unit square. Then two independent standard normal random variables can be generated as $N_1 = \sqrt{-2 \log (U_1)} \sin (2\pi U_2)$ and $N_2 = \sqrt{-2 \log (U_1)} \cos (2\pi U_2)$.

P.S. Any software with an intrinsic normal distribution function will also do the trick.

Last edited: Sep 5, 2005
3. Sep 6, 2005

### Watts

Explain

Explain intrinsic normal distribution function(the intrinsic part).

Last edited: Sep 6, 2005
4. Sep 6, 2005

### lurflurf

The obvious method would be to generate uniform ramdon numbers on [0,1] then invert the normal CDF, but that is not computationally practical. What is often done is using the law of large numbers. The average of a large number of nonpathological random variables will be normal. Uniform randoms on [0,1] work well and are often the basis for other distributions. Also as was mentioned one could use a program/library that includes a random normal generator.

5. Sep 6, 2005

### HallsofIvy

Staff Emeritus
"Intrinsic" here just means that the software has a built in function that will calculate the normal distribution for you.