Monte Carlo Technique MCT

In Section 1.4, the MCT was introduced in general terms as an important numerical tool for studying the relationship of variables in complex systems of equations. Here, the algorithm will be presented in detail, and a more complex example will be worked. 

MCT allows one to choose any conceivable error distribution for the variables, and to transform these into a result by any set of equations or algorithms, such as recursive (e.g., root-finding according to Newton) or matrix inversion (e.g., solving a set of simultaneous equations) procedures. Characteristic error distributions are obtained from experience or the literature, e.g.. Ref. 95. 

In practice, a normal distribution is assumed for the individual variable. If other distribution functions are required, the algorithm z = /(CP) in Section 5.1.1, respectively the function FNZ() in Table 5.16 has to be appropriately changed. 

The starting point is the (pseudo-) randomization function supplied with most computers it generates a rectangular distribution of events, that is, if called many times, every value between 0 and 1 has an equal probability of being hit. For our purposes, many a mathematician s restraint regarding randomization algorithms (the sequence of numbers is not perfectly random because of serial correlation, and repeats itself after a very large number of 

Fewer than that very large number of cycles are used for a simulation (no repeats), and 

The randomization function is initialized with a different seed every time the program is run. 

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