Development of the Spatial Credibility Model - Cont.

  • In order to determine the coefficients, the partial derivations of the expected value with respect to the coefficients are set to zero, which produces the following equations:

    (1) E(Xt0) = a0 + ?i,u aiu E(Xiu)

    (2) Cov(Xt0, Xjv) = ?i,u aiu Cov(Xiu, Xjv)

    for each j and v. The county t is assumed to be fixed.

  • Equation 1 can be evaluated as:

    m = a0 + ?i,u aiu m

    which yields:

    a0 = m (1 - ?i,u aiu)

  • Notice that the sum of the coefficients equals 1.00 as in classical credibility if a0 is replaced by ma0.

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