I was working on my final assignment, and I raised Box Muller Gaussian Distribution method to look for random numbers in unity software.
I am very confused about the gaussian distribution function on the pseudocode that I found in one of the journals.
Pseudocode algoritma Box-Muller(Sukajaya dkk., 2012) :
a. Generate uniform random number u, v in range [-1, 1]
b. Calculate s = u2 + v2
c. Looping step 2 until s < 1
d. Find normal random numbers `z0 = u. √((-2lns)/s)` and z1 = v . √(- (-2lns)/s)
I think the pseudocode only talks about the Box Muller and the Gaussian Distribution function is only for displaying diagrams of randomized numbers.
The Box-Muller algorithm does not contain a direct implementation of the Gaussian density formula. Instead, it produces outcomes which (cumulatively) follow that density. The results z0 and z1 produced by the algorithm are two independent Gaussian random values. If you iterate the algorithm hundreds or thousands of times and build a histogram of all the z values, it will start looking like the bell-shaped curve of a Gaussian distribution. The math behind it is beyond the scope of a StackOverflow post, so I'm going to advise that you just push the "I believe!" button, or see the Wikipedia article if you want more explanation and links to various original sources.
I'm not sure what you mean when you say "the Gaussian Distribution function is only for displaying diagrams of randomized numbers." The Gaussian is one of the most important modeling distributions out there because sums of values from all other distributions with finite variance will converge to the Gaussian in distribution. That means if you're studying averages (which are built from sums) or aggregates of lots of little errors, the Gaussian distribution does a great job of characterizing the results.