Normal Distribution

Normal (or Gaussian) distribution is described with probability density function:

Where:

μ. Mean of a random value.
σ. Standard deviation of random value.

To model normally distributed random values, the Box-Muller transform is used that enables the user to transform uniformly distributed random values to random values with standard normal distribution.

To generate the X vector (with dimension n) of pseudo-random values that follow normal distribution and have parameters μ and σ, the following operations need to be executed:

1. Generate two vectors V1 and V2 (with dimension n) of independent pseudo-random values, which elements are uniformly distributed at the interval (0, 1).

2. Get the U vector, which elements are implementations of a normally distributed random value with the 0 mean and the 1 variance, they are calculated as .

3. Get the required vector X by the formula: .