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Development of the Spatial Credibility Model - Cont
Defining bi = ?v aiv and summing both sides of equation 4 over v produces:
n f(t,j) = ?i g(i,j) ?v aiv + n ?i f(i,j) ?u aiu
n f(t,j) = ?i g(i,j) bi + n ?i f(i,j) bi = ?i bi [g(i,j) + n f(i,j)]
which represents N equations (j = 1 to N) in N unknowns bi. It should be observed that the values of bi depend on the covariance functions f and g, but not on the loss costs. We will assume that these equations can be solved for the values of bi.
Substituting the known values of bi into equation 4 yields:
(5) f(t,j) = ?i aiv g(i,j) + ?i bi f(i,j)
?i aiv g(i,j) = f(t,j) - ?i bi f(i,j)
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