MAS-2 Flashcards Updated Spring 2025
1. Standard For Full
N(c) = [Z(1-(alpha/2)) / k]^2 * [(sig-
Credibil- ity : Number of
ma^2)(n)/mu(n) + C(x)^2]
claims
For frequency only: Set C(x)^2 = 0
2. Standard For Full Credi-
For severity only: set [sigma^2(n) /
bility : Number of
claims freq/sev
3. Standard For Full mu(n) ] = 0 N(e) = [Z(1-(alpha/2)) / k]^2
Credibil- ity : Number of
exposures
* [C(s)^2]
4. Formula relating N(c), N(e) N(c) = N(e) / mu(n)
5. Partial Credibility Factor U = Z(D) + (1-Z)M
6. Square Root Rule Z = sqrt[ n /N(e) ] = sqrt[ n * mu(n) /N(c)
]
7. Conjugate Prior Shortcut:
Poisson/Gamma 10. Conjugate Prior Shortcut:
Geometric/Beta
8. Conjugate Prior Shortcut:
Exponential/Gamma
9. Conjugate Prior Shortcut:
Binomial/Beta
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, MAS-2 Flashcards Updated Spring 2025
Model: Poisson(lambda)
Prior: lambda ~
Gamma(a,b) --> mean
=ab, var= ab^2
Posterior: (lambda |
data) ~ Gamma(a*, b*)
a* = a + sum[Xi] from 1
to n
b* = [ (1/b) + n ]^(-1)
Model:
exponential(lambda) -->
mean = lamb- da^-1
Prior: lambda ~
Gamma(a,b) --> mean
=ab, var= ab^2
Posterior: (lambda |
data) ~ Gamma(a*, b*)
a* = a + n
b* = [ (1/b) + sum[Xi] from
1 to n ]^(-1)
Model:
binomial(m, q,
(1-q) ) Prior: q
~ Beta(a, b,
1)
Posterior: ( q | data
) ~ Beta(a*, b*, 1)
a* = a + sum[Xi]
from 1 to n
b* = b + [ n*m - (sum[Xi]
from 1 to n) ]
Model: geometric (
p(success) = q) -->
mean= (1-q) / q
Prior: q ~ Beta(a, b, 1)
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, MAS-2 Flashcards Updated Spring 2025
Posterior: ( q | data ) ~ Beta(a*,
b*, 1) a* = a + n
b* = b + sum[Xi] from 1 to n
11. Expected Hypothetical ¼x)(=E[ E[ X | ¸ ]]
Mean [EHM]
12. Expected Process ¼P(V ) = E[ var[X | ¸ ]]
Vari- ance [EPV]
13. Variance of sigma^2(HM) =Var[ E[X | ¸]]
Hypothetical Mean
[VHM]
14. Buhlmann K , Z K = ¼P(V) /
sigma^2(HM) Z =
n / (n+k)
15. Variance of a MA process sigma^2(x) = sigma^(w) * sum[ B^2(i) ]
16. MA(q) Autocorrelation for- Bq / [ (B0)^2 + (B1)^2 + ... (Bq)^2 ] =
ACF(q)
mula
17. Linkages Single - Smallest dissimilarity is taken.
Results in lower fusion heights
Centroid - Dissimilarities of centroids is
taken. Can results in dendrogram
inversions Average Linkage- Average of
dissimilarities.
Balanced dendrogram
Complete Linkage- Greatest dissimilarity
taken. balanced dendrogram with higher
fusions
18. Boosted Predictions Y_hat = lambda* (y_hat_1 + y_hat_2 + ...
for- mula + y_hat_n)
Thus, lambda = Y_hat / sum[Y_hat_i]
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1. Standard For Full
N(c) = [Z(1-(alpha/2)) / k]^2 * [(sig-
Credibil- ity : Number of
ma^2)(n)/mu(n) + C(x)^2]
claims
For frequency only: Set C(x)^2 = 0
2. Standard For Full Credi-
For severity only: set [sigma^2(n) /
bility : Number of
claims freq/sev
3. Standard For Full mu(n) ] = 0 N(e) = [Z(1-(alpha/2)) / k]^2
Credibil- ity : Number of
exposures
* [C(s)^2]
4. Formula relating N(c), N(e) N(c) = N(e) / mu(n)
5. Partial Credibility Factor U = Z(D) + (1-Z)M
6. Square Root Rule Z = sqrt[ n /N(e) ] = sqrt[ n * mu(n) /N(c)
]
7. Conjugate Prior Shortcut:
Poisson/Gamma 10. Conjugate Prior Shortcut:
Geometric/Beta
8. Conjugate Prior Shortcut:
Exponential/Gamma
9. Conjugate Prior Shortcut:
Binomial/Beta
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, MAS-2 Flashcards Updated Spring 2025
Model: Poisson(lambda)
Prior: lambda ~
Gamma(a,b) --> mean
=ab, var= ab^2
Posterior: (lambda |
data) ~ Gamma(a*, b*)
a* = a + sum[Xi] from 1
to n
b* = [ (1/b) + n ]^(-1)
Model:
exponential(lambda) -->
mean = lamb- da^-1
Prior: lambda ~
Gamma(a,b) --> mean
=ab, var= ab^2
Posterior: (lambda |
data) ~ Gamma(a*, b*)
a* = a + n
b* = [ (1/b) + sum[Xi] from
1 to n ]^(-1)
Model:
binomial(m, q,
(1-q) ) Prior: q
~ Beta(a, b,
1)
Posterior: ( q | data
) ~ Beta(a*, b*, 1)
a* = a + sum[Xi]
from 1 to n
b* = b + [ n*m - (sum[Xi]
from 1 to n) ]
Model: geometric (
p(success) = q) -->
mean= (1-q) / q
Prior: q ~ Beta(a, b, 1)
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, MAS-2 Flashcards Updated Spring 2025
Posterior: ( q | data ) ~ Beta(a*,
b*, 1) a* = a + n
b* = b + sum[Xi] from 1 to n
11. Expected Hypothetical ¼x)(=E[ E[ X | ¸ ]]
Mean [EHM]
12. Expected Process ¼P(V ) = E[ var[X | ¸ ]]
Vari- ance [EPV]
13. Variance of sigma^2(HM) =Var[ E[X | ¸]]
Hypothetical Mean
[VHM]
14. Buhlmann K , Z K = ¼P(V) /
sigma^2(HM) Z =
n / (n+k)
15. Variance of a MA process sigma^2(x) = sigma^(w) * sum[ B^2(i) ]
16. MA(q) Autocorrelation for- Bq / [ (B0)^2 + (B1)^2 + ... (Bq)^2 ] =
ACF(q)
mula
17. Linkages Single - Smallest dissimilarity is taken.
Results in lower fusion heights
Centroid - Dissimilarities of centroids is
taken. Can results in dendrogram
inversions Average Linkage- Average of
dissimilarities.
Balanced dendrogram
Complete Linkage- Greatest dissimilarity
taken. balanced dendrogram with higher
fusions
18. Boosted Predictions Y_hat = lambda* (y_hat_1 + y_hat_2 + ...
for- mula + y_hat_n)
Thus, lambda = Y_hat / sum[Y_hat_i]
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