This approach is called stratified sampling. With reasonably high number of layers (tens or hundreds), the created quantity xwill have the proper probability distribution. The interval (0 1) is divided into several layers of the same width, and the xvalues are calculated via the inverse transformation ( F –1) for the Fvalues corresponding to the center of each layer. The difference is that LHS creates the values of Fnot by generating random numbers dispersed in chaotic way in the interval (0 1), but by assigning them certain fix values. The basic idea of LHS is similar to the generation of random numbers via the inverse probabilistic transformation (3) and Figure 2 shown in Chapter 15. This problem can appear especially if the output function depends on many input variables.Ī method called Latin Hypercube Sampling (LHS) removes this drawback. Sometimes, more numbers are generated in one region than in others, and the generated quantity has thus somewhat different distribution than demanded. Second, it can happen that the generated random numbers of distribution function F(which serves for the creation of random numbers with nonstandard distributions) are not distributed sufficiently and regularly in the definition interval (0 1). If the output quantity must be obtained by time-consuming numerical computations, the simulations can last a very long time, and the response surface method is not always usable. First, it usually needs a very high number of simulations. The Monte Carlo method has two disadvantages.
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