Characterizing Distributions by Moment Existence and Tail Behavior
Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) lesson in Severity, Frequency, and Aggregate Models. 11 min read, ~1,632 words.
Pareto: iff. Alpha is a ceiling on moment order (variance requires ). Heavy-tailed: MGF does not exist for any; survival decays slower than any exponential. Pareto, lognormal, Weibull( ). Light-tailed: MGF exists for some. Exponential, gamma, Weibull( ). Lognormal is the key edge case: all moments finite, but still heavy-tailed...
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What this lesson covers
- Content
- Example 1
- Example 2
- Common Mistakes
- Check Your Understanding
- Exam Shortcuts
Learning objectives
- 2d
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