Titel_SS06
Return Period for Extreme Events The return period TR for an extreme event may be defined by: max , 1 R (1 XT( )) TnT T Fx ...
Assessment and statistical quantification of the available data Selection of distribution function Estimation of distribut ...
Postulate a hypothesis for the distribution family. Estimate the parameters for the selected distribution on the basis of st ...
Now by plotting x against,-1(()FxX ), see also Figure 2.18 it is seen that a straight line is obtained with slope depending on t ...
Given an ordered set of observed values x( , ,..,x 12 xxN)T of a random variable the cumulative distribution function may be ev ...
(^) -1(F (x))X x F (x)X Figure 2.20: Concrete cube compressive strength data plotted in Normal distribution paper. When using p ...
By equating the k sample moments to the k equations for the moments for the random variable X a set of k equations with the k un ...
Table 2.2. Assuming that the concrete cube compressive strength is Normal distributed it is required to estimate the parameters ...
: 1 4.04 : 2 32.665 Not surprisingly the same result as the method of moments. As mentioned previously the covariance matr ...
3 rd Lecture: Bayesian Decision Analysis Aim of the present lecture The aim of the present lecture is to introduce the basic pri ...
3.1 Introduction The ultimate task for the engineer is to establish a consistent decision basis for the planning, design, manufa ...
facility. However, as the capacity of the local water reservoir is not known with certainty another option is to get the water f ...
A further analysis of the decision problem requires the numerical assessment of the preferences of the decision maker. It is ass ...
3.5 Decision Making Subject to Uncertainty Having formulated the decision problem in terms of a decision/event tree, with proper ...
The decision/event tree is illustrated in Figure 3.3 together with the expected costs (in boxes). It is seen that the action alt ...
Prior Posterior Likelihood Likelihood Prior Posterior Prior Posterior Likelihood Figure 3.4: Illustration of updating of probabi ...
True capacity of the reservoir Indicators : 1 : Less than 100 : 2 : Larger than 100 I 1 : Capacity >105 0.1 0.8 I 2 : Capacit ...
3.8 Decision Analysis with ‘Unknown’ Information - Pre-posterior Analysis Often the decision maker has the possibility to ‘buy’ ...
>? >? >? | 313 min [ | ] (100 10) [ 23 | ] 10; 100 min 0.75 (100 10) 0.25 10;100 min 85;100 85 @@ @@ @@ ...
Figure 3.6: Decision/event tree for prior and posterior decision analysis. A posterior analysis is in principle of the same form ...
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