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ASTAM FLASHCARDS (ASTAM FORMULAS AND SHORTCUTS TO REMEMBER) THESE ARE NOT PROVIDED ON THE EXAM.
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ASTAM FLASHCARDS (ASTAM FORMULAS AND SHORTCUTS TO REMEMBER) THESE ARE NOT PROVIDED ON THE EXAM.
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ASTAM FLASHCARDS(ASTAM FORMULAS
AND SHORTCUTS TO
REMEMBER) THESE
ARE NOT PROVIDED
ON THE EXAM.
Evatee 9/10/24 ASTAM
, ASTAM FLASHCARDS (ASTAM FORMULAS
AND SHORTCUTS TO REMEMBER) THESE ARE
NOT PROVIDED ON THE EXAM.
If (N ∣ λ ) ∼ Poisson (λ) where Λ ∼ Gamma (α, θ), then Answer - N ∼ Neg.
Binomial (α, θ)
If ( X ∣ θ ) ∼ Normal (θ, v) where Θ ∼ Normal (µ, a), then Answer - X ∼ Normal
(µ, v + a)
If ( X ∣ θ ) ∼ Exponential (θ) where Θ ∼ Inv. Gamma (α, β), then Answer - X ∼
Pareto (α, β).
If ( X ∣ q ) ∼ Bernoulli (q) where Q ∼ Beta (a, b, 1), then Answer - X ∼ Bernoulli
(a/(a+b))
How to splice two models together? Answer - • Integrate/sum probability
function and equate to 1
• Equate PDF at splicing point if PDF is continuous
Formula for Fraility Model Answer -
4 ways to determine tail weight for a distribution Answer - 1. Fewer positive
raw moments ⟹ heavier tail
2. If lim as x ⟹ ∞ (S1(x)/S2(x) = ∞ or
lim as x ⟹ ∞ (f1(x)/f2(x) = ∞, then numerator has a heavier tail.
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