How does one sample from a gaussian distribution without a library?

Question

I am looking to write a program that generates samples from a gaussian distribution with a certain mean and standard deviation. I am not allowed to use any library except a random number generator. Is there a trivial way that one could do that? I am familiar with techniques like rejection sampling or a mcmc approach but they might not be easy to implement without a library.

Note - The reason I am asking this question on Cross Validated instead of StackOverFlow is because I am not looking for code. I am rather looking for equations that I can convert into code.

The answer depends on what computational facilities your system supports. For instance, can you compute logarithms? Trigonometric functions? Assuming you can, the Box-Muller method is standard and simple. But why are you "not allowed"? Is this a learning exercise or an actual problem? — whuber, Jun 28 '23 at 19:30
Note that many of the procedures and principles used to generate uniform random variates from a Normal variate can be reversed to solve this problem, too. — whuber, Jun 28 '23 at 19:32
Thank you for the reply @whuber. Yes, this is an actual problem wherein I need to write code to sample from a normal distribution that doesn't build up from other libraries. — desert_ranger, Jun 28 '23 at 19:35
Again: what are you allowed? Exactly how limited is your programming environment? — whuber, Jun 28 '23 at 19:36
I am allowed to use standard trigonometric and logarthmic functions — desert_ranger, Jun 28 '23 at 19:37
Okay, then the duplicate provides some effective (and good) answers. — whuber, Jun 28 '23 at 19:40

How does one sample from a gaussian distribution without a library?

0 Answers0