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This function is returning the number of unit that we need such that some conditions are fulfilled. See Details
c_bound2(pik)
An integer value, the number of units that we need to respect the constraints.
vector of the inclusion probabilities.
The function is computing the number of unit \(K\) that we need to add such that the following conditions are fulfilled :
\(\sum_{k = 1}^K \pi_k \geq 1\)
\(\sum_{k = 1}^K 1 - \pi_k \geq 1\)
Let \(c\) be the constant such that \(\sum_{k = 2}^K min(c\pi_k,1) = n \), we must have that \( \pi_1 \geq 1- 1/c\)
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