C: Random Number Generation - What (If Anything) Is Wrong With This

Question

For a simple simulation in C, I need to generate exponential random variables. I remember reading somewhere (but I can't find it now, and I don't remember why) that using the rand() function to generate random integers in a fixed range would generate non-uniformly distributed integers. Because of this, I'm wondering if this code might have a similar problem:

//generate u ~ U[0,1]
u = (   (double)rand() / ((double)(RAND_MAX));
//inverse of exponential CDF to get exponential random variable
expon = -log(1-u) * mean;

Thank you!

Answer 1

The problem with random numbers in a fixed range is that a lot of people do this for numbers between 100 and 200 for example:

100 + rand() % 100

That is not uniform. But by doing this it is (or is close enough to uniform at least):

u = 100 + 100 * ((double)rand() / ((double)(RAND_MAX));

Since that's what you're doing, you should be safe.

Answer 2

In theory, at least, rand() should give you a discrete uniform distribution from 0 to RAND_MAX... in practice, it has some undesirable properties, such as a small period, so whether it's useful depends on how you're using it.