Titel_SS06

 Assessment and statistical quantification of the available data

 Selection of distribution function

 Estimation of distribution parameters

 Model verification

 Model updating

Typically the initial choice of the model i.e. underlying assumptions regarding distributions
and parameters may be based mainly on subjective information whereas the assessment of the
parameters of the distribution function and not least the verification of the models is
performed on the basis of the available data.

The principle for establishing a probabilistic model is illustrated in Figure 2.17.

Subjective

• Physics


• Experience


• Judgement

Frequentistic

• Data


• Experience

Distribution family

Distribution parameters

Probabilistic model

Figure 2.17: Illustration of the formulation of probabilistic models for uncertain variables.

As the probabilistic models are based on both frequentistic information and subjective
information these are Bayesian in nature.

In the following only the probabilistic modelling of random variables will be considered, but
the described approach applies with some extensions also to the probabilistic modelling of
random processes and random fields.

First the problem of choosing an appropriate distribution function family is addressed, and the
task of estimating the parameters of the selected distribution function is considered. A
statistical framework for the verification of such models is given in lecture notes for the
course on Basic Theory of Probability and Statistics in Civil Engineering.

2.12 Selection of Probability Distributions

In general the distribution function for a given random variable or stochastic process is not
known and must thus be chosen on the basis of frequentistic information, physical arguments
or a combination of both.

A formal classical approach for the identification of an appropriate distribution function on
the basis of statistical evidence is to: