Conditional distribution function

Conditional Distribution Functions and Statistical Independence.—The definition of a conditional distribution function is motivated by the following considerations. Suppose that we have been observing a time function X and that we want to obtain a quanti-... 

We shall now define the left-hand side of Eq. (3-166) to be the conditional distribution function for fa given that fa assumes the value g2... 

Complex conjugation, 492 Complex-valued random variables, 144 Compound distribution, 270 Conditional distribution functions, 148, 152... 

The physical meaning of the pair correlation function g can be elucidated by using the conditional probability concept introduced in Section 1.5.2. In analogy with Eq. (1.187), the single particle conditional distribution function in a homogeneous system is given by... 

It is important to take note of the order in which we couple each part of the potential. When the nth part has already been coupled, it has an effect on the distribution of the configurations of the solvent molecules. Therefore, in the next step we have to replace the distribution function used in the coupling of the nth part by a conditional distribution function for calculating the average in the (n+ l)th part. 

We see that relations (7.132) and (7.133) have the same form as relation (7.120). Placing X at a fixed position has an effect on the distribution of the configurations of solvent molecules around X. Therefore, when we couple the group Y at a location near X, the average work is now calculated with the conditional distribution function as shown in (7.132). The procedure outlined above may be generalized to include large molecules with many groups. We shall make use of such a procedure for proteins in section 7.11. 

The goal of indicator kriging is to estimate the conditional distribution function of the unknown concentrations, Z(x) at... 

These statistical data allow us, applying the methods and procedures given in the section 2, to formulate and to verify the hypotheses about the conditional distribution functions Hn t) of the Stena Baltica ferry operation process sojourn times On, b = 1,2,..., 17, / = b + and b = 18,/ = 1 in the state zj while the next transition is to the state Z on the base of their... 

Various conditional MDF s can be introduced for instance, the singlet conditional distribution function, for finding a particle at X3 given two particles at Xi and Xg, is... 

Next, the conditional distribution functions are introduced. For instance,... 

As in the one-component case, QabO I ") wiay be interpreted as the density of A particles in configuration X, given a B particle in a fixed configuration X ". (For more details, see Sections 2.3 and 2.4.) In a two-component system, we have four conditional distribution functions corresponding to the four pairs of species AA, AB, BA, and BB. 

The singlet conditional distribution functions in (7.29) and (7.30) have an obvious meaning. For instance, q(Xj /Rs, li, 2 = 0) denotes the singlet conditional distribution function for solvent molecules, given a solute particle at coupled to the extent li and S2 = 0. 

We now use the conditional distribution function of finding a configuration R given a system with volume V [see Eq. (1.56)]... 

Moreover, we assume the following matrix of the conditional distribution functions of the system sojourn times b,l = l, 2,3,... 

When the dependence Levy copula is in Clayton family, according to equation (3) the conditional distribution function take a form ... 

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