A transformation which transforms from a two-dimensional continuous uniform distribution to a two-dimensional bivariate normal distribution (or complex normal distribution). If x_1 and x_2 are uniformly and independently distributed between 0 and 1, then z_1 and z_2 as defined below have a normal distribution with mean μ = 0 and variance σ^2 = 1. z_1 | = | sqrt(-2 ln x_1)cos(2π x_2) z_2 | = | sqrt(-2 ln x_1)sin(2π x_2).

bivariate normal distribution | normal distribution