Sij definition
Examples of Sij in a sentence
Settlements (2004) states that “the PD for retail exposures is the greater of the one-year PD associated with the internal borrower grade to which the pool of retail exposures is assigned or 0.03%”, suggesting to enhance Equation 2.1 along the lines of Sij = max(Si + ϵij, ci) with known obligor-specific cutoffs ci.
The auxiliary random variable Sij stands for the former key while Sji is associated with the latter key.
For Merton type models, l = Φ−1 and Si = −DDi. Writing µij and σij denote the mean and standard deviation of ϵij, respectively, the above latent trait model can be written as Sij = Si + µij + σij Zij where the standardized rating errors Zij = (ϵij −µij)/σij have mean zero and unit variance.
Let Sij = l(PDij) and Si = l(PDi) denote the observed and latent scores, respectively.
Note that Di,w = Σg∈{0,1}b Ig. For the expectation we have that E [Ig] = P [g ∈ Si,g ⊕ w ∈ Sij] = P [g ∈ Si] P [g ⊕ w ∈ Sij | g ∈ Si] , Σ where we have to compute this value separately for equal and different permu- tations.
From the fact that Prob [Si = Sij] < sj holds we conclude, by Fano’s inequality, H(Si Sij) sjK + 1 for all i, hence H(SM (Sj)M ) M (sjK + 1).
Sij denotes the auxiliary random variable associated with key Kij generated by user i to be shared with user j.
The first assumption that must be employed for RCM is the Stable Unit Treatment Value Assumption (SUTVA), which states that there is no interfer- ence between observed treatment Zobs of one unit i and the potential outcomes of Sij and Yij.
We hereby describe a mathematical model of our proposed solution as follows (Figure 4.5 gives a summary of this model): Let S = {all services in a grid system} Then S = {Sij} where i = 1,.., n is the service index and j = 1,.., m is the variant index within a service.
For a matrix R ∈ Rn×n and a set of indexes I ⊂ [n] × [n], define R F,I as the ▇▇▇▇▇▇▇▇▇ ▇▇▇▇ of the matrix R calculated only on the entries with indexes in I, that is, := (i,j)∈I Similarly, for a pair of matrices R, S ∈ Rn×n, we define the inner product of the entries with indexes in I as ⟨R, S⟩£ := (iΣ,j)∈£ Rij Sij.