Actuary Certification Loss Models Flashcards
6 cards from real Actuary Certification practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
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The Bühlmann credibility formula for the credibility estimate is:
Answer: Z · X̄ + (1−Z) · μ
The Bühlmann credibility estimate is Z·X̄ + (1−Z)·μ, a weighted blend of the observed mean X̄ and the prior mean μ, where Z = n/(n+k) is the credibility factor.
In the Bühlmann credibility model, the credibility factor Z = n/(n+k) where k equals:
Answer: Expected process variance / variance of hypothetical means
k = v/a where v is the expected value of the process variance (EVPV) and a is the variance of the hypothetical means (VHM), so k = EVPV/VHM.
Which reinsurance arrangement has the reinsurer paying losses above an attachment point up to a maximum layer?
Answer: Excess of loss (per-occurrence) reinsurance
Per-occurrence excess of loss reinsurance covers losses above the cedant's retention (attachment point) up to a specified maximum per single occurrence.
The method of moments estimator equates sample moments to theoretical moments. For a one-parameter distribution, this means setting:
Answer: Sample mean = theoretical mean
With a single parameter, method of moments sets the sample mean equal to the theoretical mean E[X] and solves for the parameter.
Which goodness-of-fit test statistic compares the squared differences between observed and expected frequencies divided by expected frequencies?
Answer: Chi-square statistic
The chi-square goodness-of-fit statistic is Σ(Oi − Ei)²/Ei, measuring the discrepancy between observed and expected cell frequencies.
The Kolmogorov-Smirnov test compares:
Answer: Maximum absolute difference between empirical and fitted CDFs
The K-S statistic is Dn = sup|Fn(x) − F(x)|, the maximum vertical distance between the empirical CDF and the hypothesized CDF.