Box-Muller Transformation
A transformation which transforms from a 2-D continuous Uniform Distribution to a 2-D Gaussian BivariateDistribution (or Complex Gaussian Distribution). If 
and 
are uniformly andindependently distributed between 0 and 1, then 
and 
as defined below have a Gaussian Distribution withMean 
and Variance 
.
 |  |  | (1) |
 | |  | (2) |
This can be verified by solving for
and , | |  | (3) |
 | |  | (4) |
Taking the Jacobian yields
 | |  | |
|  | (5) |
- Jacobian Group
- Jacobi Differential Equation
- Jacobi Differential Equation (Calculus of Variations)
- Jacobi Elliptic Functions
- Jacobi Function of the First Kind
- Jacobi Function of the Second Kind
- Jacobi-Gauss Quadrature
- Jacobi Identities
- Jacobi Matrix
- Jacobi Method
- Jacobi Polynomial
- Jacobi Quadrature
- Jacobi Rotation Matrix
- Jacobi's Curvature Theorem
- Jacobi's Determinant Identity
- Jacobi's Imaginary Transformation
- Jacobi's Theorem
- Jacobi Symbol
- Jacobi Tensor
- Jacobi Theta Function
- Jacobi Transformation
- Jacobi Triple Product
- Jacobi Zeta Function
- Jacobsthal-Lucas Number
- Jacobsthal-Lucas Polynomial