Expected Value Model

If decision makers want to make a decision to get the maximal expected return under the expected value constraint, the expected value model [8] would be  

Within the model, x is an n-dimensional decision vector, is a f-dimensional random vector and its probability density function is f x, Q is the target function, gj x, and h]c x, are random constraint function, and E is the expected 

If there are multiple decision objectives, the multi-objective expected value model would be 

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From Table 6.7 and the corresponding efficient frontier plot in Figure 6.4, similar trends to Risk Model II (and also the expected value models) are observed in which decreasing values of 0 correspond to higher expected profit until a certain constant profit value is attained ( 81 770). The converse is also true in which a constant profit of 59330 is reached in the initially declining expected profit for increasing values of 0i. 

The expectancy-value model, described in the next section, combines the criteria and frameworks we have explored so far into an integrated model. 

The contextualization of chemistry content in CBL aims to increase task value by making the connection of the content with personal interest and (future) utility more obvious for the students. Following the expectancy-value-model, context-based learning should therefore have an influence on the students choice of future science activities (Bennett et al., 2007). 

Zhou et al. [61] described production planning of multi-location plant and distributors on condition that unit production cost, production capacity and demand are fuzzy parameters. They built up a fuzzy expected value model and fuzzy related chance-constrained programming model in consideration of different decision criteria and discussed a clear equivalent form of the fuzzy programming model when... 

Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Transact Euzzy Syst 10(4) 445-450... 

The first part briefly introduces the stochastic expected value programming theory. With the discussing on the expected value model which is a convex programming, Theorem 4.2 is put forward and proved. Furthermore we get the conclusion that if the expected value model is a convex programming and there exists an optimal solution, then any local optimal solution will be the global optimal solution. 

Convexity of Expected Value Model and the Properties of Solutions... 

Thus it can be seen that + (1 — is a feasible solution to (4.6) and the feasible set is convex. Therefore the expected value model (4.6) is a convex programming model. This completes the proof. ... 

In summary, if the expected value model is a convex programming model and an optimal solution exists, then any local optimal solution is the global optimal solution. 

To further verify the validity of the algorithm and the random expected value model, we simulate different values of parameters of hybrid intelligent algorithm ... 

Liu YK, Liu B (2003) A class of fuzzy random optimization expected value models. Inf Sci... 

Within this work [7] a method and model to determine the optical transfer function (OTF) for the detector chain without detailed knowledge of the internal detector and camera characteristics was developed. The expected value of the signal S0.2 is calculated with... 

Data that is not evenly distributed is better represented by a skewed distribution such as the Lognormal or Weibull distribution. The empirically based Weibull distribution is frequently used to model engineering distributions because it is flexible (Rice, 1997). For example, the Weibull distribution can be used to replace the Normal distribution. Like the Lognormal, the 2-parameter Weibull distribution also has a zero threshold. But with increasing numbers of parameters, statistical models are more flexible as to the distributions that they may represent, and so the 3-parameter Weibull, which includes a minimum expected value, is very adaptable in modelling many types of data. A 3-parameter Lognormal is also available as discussed in Bury (1999). 

The first term in the brackets is the expectation value of the square of the dipole moment operator (i.e. the second moment) and the second term is the square of the expectation value of the dipole moment operator. This expression defines the sum over states model. A subjective choice of the average excitation energy As has to be made. 

The SSH model (Eq. (3.2)) is, essentially, the model used by Peierls for his discussion of the electron-lattice instability [33]. Its ground state is characterized by a non-zero expectation value of the operator. 

For ionic compounds, crystal field theory is generally regarded a sufficiently good model for qualitative estimates. Covalency is neglected in this approach, only metal d-orbitals are considered which can be populated with zero, one or two electrons. To evaluate (Vzz)vai 4t the Mdssbauer nucleus, one may simply take the expectation value of the expression — e(3cos 0 — for every electron in a valence orbital i/, of the Mdssbauer atom and sum up,... 

On the other hand, the permanent EDM of an elementary particle vanishes when the discrete symmetries of space inversion (P) and time reversal (T) are both violated. This naturally makes the EDM small in fundamental particles of ordinary matter. For instance, in the standard model (SM) of elementary particle physics, the expected value of the electron EDM de is less than 10 38 e.cm [7] (which is effectively zero), where e is the charge of the electron. Some popular extensions of the SM, on the other hand, predict the value of the electron EDM in the range 10 26-10-28 e.cm. (see Ref. 8 for further details). The search for a nonzero electron EDM is therefore a search for physics beyond the SM and particularly it is a search for T violation. This is, at present, an important and active held of research because the prospects of discovering new physics seems possible. 

When it is employed to specify an ensemble of random structures, in the sense mentioned above, the MaxEnt distribution of scatterers is the one which rules out the smallest number of structures, while at the same time reproducing the experimental observations for the structure factor amplitudes as expectation values over the ensemble. Thus, provided that the random scatterer model is adequate, deviations from the prior prejudice (see below) are enforced by the fit to the experimental data, while the MaxEnt principle ensures that no unwarranted detail is introduced. 

For acute releases, the fault tree analysis is a convenient tool for organizing the quantitative data needed for model selection and implementation. The fault tree represents a heirarchy of events that precede the release of concern. This heirarchy grows like the branches of a tree as we track back through one cause built upon another (hence the name, "fault tree"). Each level of the tree identifies each antecedent event, and the branches are characterized by probabilities attached to each causal link in the sequence. The model appiications are needed to describe the environmental consequences of each type of impulsive release of pollutants. Thus, combining the probability of each event with its quantitative consequences supplied by the model, one is led to the expected value of ambient concentrations in the environment. This distribution, in turn, can be used to generate a profile of exposure and risk. 

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