LHS LATIN HYPERCUBE SAMPLING SOFTWARE

The improvement offered by LHS over Monte Carlo can be easily demonstrated. Since the number of iterations n is also the number of intervals, each interval will only have been sampled once and the distribution will have been reproduced with predictable uniformity over the F(x) range. This process is repeated for all of the iterations.

The process is repeated for the second iteration but the interval used in the first iteration is marked as having already been used and therefore will not be selected again. X = G(F(x)) is calculated for that value of F(x).

In practice, the second half of the first random number can be used for this purpose, reducing simulation time. In the first iteration, one of these intervals is selected using a random number.ДЄ second random number is then generated to determine where, within that interval, F(x) should lie. The bands can be seen to get progressively wider towards the tails as the probability density drops away. The probability distribution is split into n intervals of equal probability, where n is the number of iterations that are to be performed on the model.В The Figure 1 below illustrates an example of the stratification that is produced for 20 iterations of a Normal distribution. It uses a technique known as 'stratified sampling without replacement' ( Iman et al., 1980) and proceeds as follows:

LHS LATIN HYPERCUBE SAMPLING SOFTWARE

In fact, we would say that it is one of the features that is essential in any risk analysis software package. Latin Hypercube sampling, or LHS, is an option that is now available for most risk analysis simulation software programs.

Lhs latin hypercube sampling