The following distribution functions are used for stochastic allocation:

 

• Normal distribution

The normal distribution has the density function:

 

Input values for the generation of normally distributed values (x) are:

 

σ = Standard deviation

σ² = Variance

µ = Mean value

 

Density function for approx.. 18,000 values generated with the normal distribution

 

• Log-normal distribution

With the log-normal distribution, the logarithm of the generated values is normally distributed:

 

 

Input values for generating lognormally distributed values (x > 0) are:

 

σ = Standard deviation

σ² = Variance

µ = Mean value

 

Density function for approx.. 18,000 values generated with the log-normal distribution

 

• Exponential distribution (uncorrelated generation only)

The exponential distribution has the density function for x > 0::

 

The input value for generating exponentially distributed values x > 0 is the mean value μ.

 

Density function for approx.. 18,000 values generated with an exponential distribution

 

Anisotropic K-values