Create new distributions by multiplication by a constant, raising to a power, exponentiation, mixing and splicing.
Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lesson in Severity Models. 26 min read, ~3,886 words.
Multiplication: same family,. Inflation tool. Power: exponential to Weibull (τ 0); gives the inverse family. Exponentiation: normal to lognormal with the same parameters. Mixing: weight pdfs by a mixing distribution. Gamma-mixed exponential = Pareto. Splicing: piecewise density with weights summing to 1, continuity at breakpoints optional. Mean excess loss measures...
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What this lesson covers
- Content
- Example 1
- Example 2
- Example 3
- Example 4
- Example 5
- Common Mistakes
- Key Takeaways
- Exam Shortcuts
Learning objectives
- 1b
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