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Development of the Spatial Credibility Model - Cont
The first term on the right side of equation 3 can also be evaluated:
E[Cov(Xiu, Xjv|Ri,Rj)] = E[Cov(m + Ri + Qiu, m + Rj + Qjv|Ri,Rj)] = E[Cov(Qiu, Qjv)]
When u ? v, the independence of the experience between different years implies that the covariance of the random fluctuation term is 0. When u = v, it will be assumed that:
E[Cov(Qiu, Qju)] = g(d(i,j))
That is, the expected intertemporal covariance is a function of the distance between the two counties. For simplicity, g(d(i,j)) will be replaced by g(i,j). By defining ?uv as 0 when u ? v and 1 when u = v, the first term on the right side of equation 3 can be expressed as:
E[Cov(Xiu, Xjv|Ri,Rj)] = ?uvg(i,j)
As a result, equation 3 can be expressed as:
Cov(Xiu, Xjv) = ?uvg(i,j) + f(i,j)
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