Processing of Random Variables

Above a number of phenomena were mentioned whose behaviour is random (e.g. behaviour of a released gas, weather conditions etc.). The variables describing them adopt a particular value with a certain probabihty and are therefore described by probability distributions. Furthermore there are phenomena which can be described by several models. This points to modelling uncertainties. 

In order to propagate modelling uncertainties and uncertainties stemming from the stochastic character of variables or insufficient knowledge of variables through the calculations and account for them in the final results the Monte Carlo simulation is used (cf. Example 4.5 and [14]). 

As already explained, Monte Carlo simulation is based on repeating a calculation several times (N times). Each calculation is called a trial. In each trial a concrete value (realization) is generated for any random variable on the basis of its corresponding distribution. If several models for one phenomenon are available a concrete model is selected on the basis of a probability believed to represent its relevance. In order to generate random variables from different probability distributions, random variables uniformly distributed on [0, 1] are transformed into random variables from the distribution in question (cf. [14] and Sect. 10.9). 

The total of N results forms a histogram. For simplicity s sake this histogram is approximated by a log-normal distribution. 

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