A method for generating random numbers numbers with a Gaussian distribution (also known as a normal distribution) using numbers with a uniform distribution.
The basic form of the transformation starts with two uniformly distributed random numbers x1 and x2. Then we can generate two normally distributed random numbers y1 and y2 as the following:
y1 = sqrt(-2ln(x1))cos(2πx2)
y2 = sqrt(-2ln(x1))sin(2πx2)
The new distribution has a mean of zero and a standard distribution of one.