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Extra resources for Clustered Encouragement Designs with Individual Noncompliance Bayesian Inference with Randomization, and Application to Advance Directive Forms

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M(s)) is defined in a single way by the system Λ(s) = Λ(s)Θ(s), Θ(s) indivisible. 5) with indivisible matrix ||ν(s, s∗)||s,s∗∈S are true. 15) Limit Distributions in Queueing Networks with Different Types... 27 where N = (n s , s ∈ S) is the vector containing vectors of customers numbers in the network nodes n s = (ns1 , . , nsm ) for all customers types, Y S = Y × . . 6). So a changeover from a processing of one customers type to another is independently on numbers of customers of different types in the network nodes.

M and µ1 , . , µr . Denote by r Θ = ||θij | |m i,j=0 , Θ = |θij |i,j=0 the route matrixes of the networks G, G . Define m the superposition G = G ⊗ G of the networks G, G by a replacement of the node gm in G by the network G . Here an input flow (output flow) of the network G is created from customers arriving (departing) to the node (from the node) gm . In the network G the input flow is Poisson with the single intensity, the nodes set is {g0 , g1 , . . , gm+r−1 } = {g0, g1, . . , gm−1, g1, .

Network with “negative” customers flow Consider the network G with the structure s0 and with an additional Poisson input flow with the intensity λ− . A customer of the additional flow (call this customer m “negative”) arrives to the node k server with the probability δk , δk = 1, and k=1 immediately departs from the network capturing a main flow customer if it is at this server. Denote this network structure by − − − s− 0 = ({1, . , m}, λ, (µ1 , . . , µm ), Θ , Y ) − m − − where µ− j = µj + λ δj , j = 1, m, Θ = ||θij ||i,j=0 , and m − θ0j = θ0j , j=0, m, − θij µi − − = θij − , i, j=1, m, θi0 = 1− θij , i=1, m.

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Clustered Encouragement Designs with Individual Noncompliance Bayesian Inference with Randomization, and Application to Advance Directive Forms by Frangakis C.E.


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