Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

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106 Actuarial Modelling of Claim Counts Table 2.13 Results of the Negative Binomial regression model with panel data, Portfolio B. Variable Level Coeff Std error 95 % conf limit t Pr > t Intercept −12277 00646 −13542 −11011 −1901
Risk Classification 107 PrN i1 = k i1 N iTi = k iTi ( ) ∫ + Ti ( ∏ 1 = PrN it = k it i = √ exp − 1 ) 0 2 3 2 − 12 d t=1 Again, numerical methods are needed to obtain the solutions and the SAS R /STAT procedure NLMIXED can be used to maximize the log-likelihood. The fit of the Poisson-Inverse Gaussian model is described in Table 2.14. We get ̂ = 05575. The variance-covariance matrix of the estimated regression coefficients and dispersion parameter ̂ is ⎛ ⎞ 0004216 −0000289 −0003723 −0003709 −0000534 −0000567 0000115 −0000289 0000830 −0000002 −0000004 0000000 0000009 −0000002 −0003723 −0000002 0004118 0003755 −0000097 −0000058 −0000027 ̂̂ = −0003709 −0000004 0003755 0004193 −0000069 −0000052 0000011 ⎜ −0000534 0000000 −0000097 −0000069 0001152 0000616 0000030 ⎟ ⎝ −0000567 0000009 −0000058 −0000052 0000616 0001169 −0000010 ⎠ 0000115 −0000002 −0000027 0000011 0000030 −0000010 0002492 The log-likelihood is equal to −19 6437 and Type 3 analysis gives Source DF Chi-square Pr>Chi-sq Gender 1 54 00201 Age ∗ Power 2 1488
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Contents Foreword Preface Notation
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Contents vii 2.4 Overdispersion 79
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Contents ix 4.2.3 Trajectory 170 4.
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Contents xi 7.4 Numerical Illustrat
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Part I Modelling Claim Counts Actua
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Part III Advances in Experience Rat
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8 Transient Maximum Accuracy Criter
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Transient Maximum Accuracy Criterio
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Bibliography Albrecht, P. (1983a).
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Bibliography 347 Daengdej, J., Luko
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Bibliography 349 Greenwood, M., & Y
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Bibliography 351 Norberg, R. (1976)
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Bibliography 353 Walhin, J.-F., & P
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