# Random Property

The random distribution, for Density, Poisson, Shear Modulus and Damping, can be:

• Normal distribution: (or Gaussian), is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean
• Uniform distribution: is a probability distribution where all outcomes are equally likely

There are many types of spatial variability, but all refer to the following formula:

where:

• XRND = random parameter to be used in the calculation
• μ = average value
• σ = standard deviation capable of disturbing the distribution and ε is the random variable with zero average and one for the standard deviation.

The algorithm proposed by Box and Muller generates the Gaussian distribution (Box, G. E. P.; Muller, Mervin E. A Note on the Generation of Random Normal Deviates. Ann. Math. Statist. 29 (1958)

where:

• ε1 and ε2 are two non-correlated (pseudo) random variables with zero mean and unit standard deviation.

The parameter according to numerical value of XRND it is into the range is calculated:

For each parameter, the average value and the range of variation (Minimum and Maximum value) is defined. It is possible to use a percentage of variation both minimum and maximum value are automatically calculated as ± (%) on average value.