Estimate the parameters for severity, frequency, and aggregate distributions using Bayesian Estimation.
Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lesson in Construction and Selection of Parametric Models. 9 min read, ~1,289 words.
Posterior ∝ Prior × Likelihood. The normalizing constant is whatever makes the posterior integrate to 1. Bayes estimate under squared-error loss is the posterior mean. Under absolute-error loss it is the posterior median. Under 0-1 loss it is the posterior mode. Conjugate pairs collapse the work: Gamma prior + Poisson...
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- Example 1
- Example 2
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Learning objectives
- 4d
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