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

356 Actuarial Modelling of Claim Counts
Negative Binomial
credibility model 131–5, 144, 148, 151–2
distribution 28–31, 45–6, 281, 284, 336
regression 83–6, 105–6, 238
Offset 73, 101
Optimal retention 220–1, 247–9, 251–4, 257–8
Panjer algorithm 279–84, 287, 330–2
Perron-Froebenius theorem 175
Poisson
distribution 15–17, 45–6, 54–6, 172–3,
229–30, 281, 283
process 17–21
regression 64–79, 94–101, 229–30, 237–8
Poisson-Inverse Gaussian
distribution 32–3, 45–6
regression 86–7, 106–7
Poisson-LogNormal
distribution 34, 45–6
regression 87–8, 107–8
Regularity 175, 176, 179, 273
Score test 43, 82–3
Special bonus rule 200–8
Specification error 72–3, 80
Total variation distance 183–4, 208–13, 295–6,
308, 315
Vuong test 43–4, 46, 89, 109–10
Wald
confidence interval 69
test 42–3