Compare two distributions based on various characteristics of their tails, including moments, ratios of moments, limiting tail behavior, hazard rate functions, and mean excess functions.
Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lesson in Severity Models. 25 min read, ~3,799 words.
Heavier tail = larger moments, faster-growing moment ratios, slower-decaying survival, decreasing or flatter hazard, increasing mean excess. Existence of moments: if is infinite for some, the tail is heavier than any distribution with all moments finite, yet lognormal has every moment finite and is still heavy-tailed. Limit ratio test: means...
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What this lesson covers
- Content
- Example 1
- Example 2
- Example 3
- Common Mistakes
- Check Your Understanding
- Exam Shortcuts
Learning objectives
- 1d
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