Titel_SS06
based on the evaluation of the respective sample statistics, see Table 2.6. For this set of data there are no outside values as ...
2.8 Uncertainties in Engineering Problems For the purpose of discussing the phenomenon uncertainty in more detail let us initial ...
extreme water levelsObserved annual Model for annual extremes Regression model to predict future extremes extreme water levelPre ...
This transition of the type of uncertainty has a significant importance because it facilitates that the uncertainty is reduced b ...
Figure 2.11: Illustration of A) a cumulative distribution function and B) a probability density function for a continuous random ...
Moments of Random Variables and the Expectation Operator Probability distributions may be defined in terms of their parameters o ...
The relevance of the different distribution functions given in Table 2.7 in connection with the probabilistic modelling of uncer ...
Distribution type Parameters Moments Beta, axb 11 1 () ()() () rt X rt rt x abx fx rt ba + ++ ...
Standard Normal Normal X Shift Scaling 0 1 Y Y Standard Normal Normal X Shift Scaling 0 1 Y Y Figure 2.13: Ill ...
^22222 222 22 () 2 2 =2 XXXX XXX Var X E X E X X E X E X EX EX X (2.37) B ...
of one variable is large compared to its mean value the outcome of the other variable is likely to be small compared to its mean ...
FxX 1 () 112 F xxf xdxXX 12 ( ) ( ) X 2 22 (2.49) The conditional moments of jointly distributed continuous random varia ...
The probability of more than one event in the interval [, is a function of a higher order term of 2 t for 2t 0. tt 2 t E ...
Continuous Random Processes A random process X()t is as mentioned a random function of time meaning that for any point in time t ...
Typically the correlation function is an exponentially decaying function in time. Having defined the mean value function and the ...
Figure 2.15: Time series of recorded daily maximal water levels together with 5 days (arbitrary point in time) and 10 days maxim ...
In the same way the cumulative distribution function of the largest extreme in a period of , may be determined from the cumulati ...
with corresponding probability density function: max fXT, ( )xxux 55 exp( ( ) exp( 5 ( u))) (2.69) which is also denoted t ...
Type II Extreme Maximum Value Distribution – Frechet max For cumulative distribution functions downwards limited at zero and upw ...
min (^22) min 2 1 ()(1) 2 ()(1)(1) T T X X u k u kk ' ' ' + + + (^89) 1 (2.83) Distribution type Parameters M ...
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