Options to fill Sample Clauses

Options to fill the transition matrices in one event and in one time unit‌‌ The transition probabilities in one earthquake (Pi, j ) needed to fill the matrix in Equation (4) , lying at the core of the model, can be computed following two (alternative) approaches. The first one is that of Equation (5), in which each Pi, j terms computed via state- dependent fragilities (i.e., transition probability from a state to a worse one, given a specific value of earthquake intensity) times the distribution of intensity in one earthquake. Equation (12) shows how to retrieve the vulnerability term of Equation (5) from state- dependent fragility curves (at the right hand side). P ⎡⎣ j − th state i − th state ∩ IM = z ⎦⎤ = P ⎣⎡ j − th state or worse i − th state ∩ IM = z ⎦⎤ + (12) −P ⎣⎡ ( j +1) − th state or worse i − th state ∩ IM = z ⎤⎦ , j ≥ i It may be interesting to note that, using state-dependent fragility curves, Equation (7) may be rewritten as in Equation (13), a format common in PBEE, where dλim ( z ) is the absolute value of the derivative of the hazard curve for the site of the construction [5]. ν E ⋅ Pi, j = ∫ P ⎣⎡ j − th state i − th state ∩ IM = z ⎦⎤ ⋅ dλim ( z ) ,