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

Index
Binomial distribution 13–15, 271–2, 281,
333
Bonus hunger 51–2, 220–1, 246–54, 257–8
Chapman-Kolmogorov equations 174
De Pril algorithm 330–3, 334, 341
Deductible 168–9, 251, 276–91
Deviance 71, 72, 75
Deviance residuals 72, 77
Efficiency 220, 257, 307, 314, 318
De Pril 242–6
Loimaranta 240–3
Eigenvalue 175, 184, 295
Eigenvector 175, 179
Ergodicity 176, 273
Exposure-to-risk 20, 44–5, 53, 56, 73, 93
Financial equilibrium 123, 130, 135, 167, 186,
197, 202, 205, 305, 314, 318, 333–5, 340–1,
342
Fisher
information matrix 38, 40, 69, 73, 104
score 36, 67–8
Gamma
distribution 28, 29, 230
regression 231–2
GEE 101–5
Generalized Pareto
distribution 224–9
index 224–6
Gertensgarbe plot 225–6
Information criteria
AIC 43, 110
BIC 43, 110
Interaction 58–9, 62–3, 74
Inverse Gaussian
distribution 31–2, 233
regression 233–4
Kolmogorov distance 208–13
Large claim 223–30, 256–7
Lemaire algorithm 251–4
Likelihood ratio
confidence interval 69
test 41–2, 45, 72, 76, 82
LogNormal
distribution 34
regression 235–6, 246–9
Mixed Poisson
credibility model 126–8, 155–8
discrete credibility model 135–6, 193–4
distribution 24–8, 46, 270–2, 278, 326
process 25
regression 80–1, 260–3
Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems
S. Pitrebois and J.-F. Walhin © 2007 John Wiley & Sons, Ltd
M. Denuit, X. Maréchal,