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). This can be verified by solving for x_1 and x_2, x_1 | = | e^(-(z_1^2 + z_2^2)/2) x_2 | = | 1/(2π) tan^(-1)(z_2/z_1).

bivariate normal distribution | normal distribution