I would like to create a random number generator for the normal distribution via using a uniform linear congruential generator (on uniform distribution) and the inversion method.
However, I'm getting stuck at the final state. Please correct my understanding at any point!
Say i have an LCG, which generates numbers from 0 - 1. It follows a uniform distribution of (0,1).
Now, I want my subsequent normal distribution (X) to follow the same range, so it's standard normal, hence i normalize the area
Using taylor series as this cannot be integrated, I get
However, now I'm stuck. even if i integrate this, I cannot invert this to y = f(x) due to the powers of y. Am I even going about this right?
Any help will be much appreciated! thank you!