Loss Models, 5th Edition

Index

A

• (a, b, 0) class of distributions, 88, 506
• (a, b, 1) class of distributions, 92, 507
  • estimation, 264
• actuarial exposure, 340
• aggregate loss distribution, 150
  • approximating distribution, 171
  • compound negative binomial–exponential, 167
  • direct calculation, 172
  • distribution function, 152
  • exponential severity, 168
  • individual risk model, compound Poisson approximation, 193
  • moment generating function, 153
  • moments, 153
  • probability generating function, 153
  • recursive formula, 173, 515
    • compound frequency, 175
    • computational issues, 177
    • construction of arithmetic distributions, 179
    • continuous severity, 178
    • undiscretization, 518
  • recursive method, 172
  • simulation, 480
• aggregate loss model, 148
  • advantages, 149
• Akaike Information Criterion, 374
• Anderson–Darling test, 363
• anniversary-to-anniversary mortality study, 342
• arithmetic distribution, 179
• asymptotically unbiased, 207
  • maximum likelihood estimator, 243

B

• bandwidth, 334
• Bayesian central limit theorem, 282
• Bayesian estimation, 275
  • Bayes estimate, 279
  • credibility interval, 280
  • highest posterior density (HPD) credibility set, 281
  • improper prior distribution, 276
  • joint distribution, 276
  • loss function, 279
  • marginal distribution, 276
  • model distribution, 276
  • posterior distribution, 277
  • predictive distribution, 277, 408
  • prior distribution, 275
• Bayesian Information Criterion, 374
• Bernoulli distribution, 88
• beta–binomial distribution, 286
• beta distribution, 503
• beta function, 491
  • incomplete, 490
• bias, 205
• binomial-beta ...