SOA Exam Stam - MLE and Variance with all Correct &
100% Verified Answers| Latest Update| Already Graded A+
1. Truncated Data Data above/below the truncation point is missing
left truncated = P(x=x|x>d) = fx / Sd
(condition on exceeding d, common likelihood for deductibles!!)
if loss less than d, policyholder receives no reimbursement, so loss
isnt reported. losses only recorded when exceeding deductible
right truncation is less common, but condition on p(x<u)
2. Censored Data Exact values are unknown
This is common with grouped data
If left-censored/censored from below, we know value is at most d, but
only recorded at d
Lx = P(x<d)
If right-censored/censored from above, value is at least u, but only
recorded as u.
Lx = Su
Common for policy limits!! Right censored is way more common.
3. Grouping Data special case of censoring
exact values
unknown Lx = Sa-
Sb
4. ALGEBRA REVIEW How can we simplify
(EXPONENTS):
L(α) =α4 /
240^α+1*100^α
1/
8
, SOA Exam Stam - MLE and Variance with all Correct &
100% Verified Answers| Latest Update| Already Graded A+
240^a+1*100^a
240^a*240^1*100^a
The constants dont attect the
likelihood, so 240^1 is not
necessary to keep in. We can
say the likelihood is
proportional without the
constant.
240^a*100^a
2/
8
100% Verified Answers| Latest Update| Already Graded A+
1. Truncated Data Data above/below the truncation point is missing
left truncated = P(x=x|x>d) = fx / Sd
(condition on exceeding d, common likelihood for deductibles!!)
if loss less than d, policyholder receives no reimbursement, so loss
isnt reported. losses only recorded when exceeding deductible
right truncation is less common, but condition on p(x<u)
2. Censored Data Exact values are unknown
This is common with grouped data
If left-censored/censored from below, we know value is at most d, but
only recorded at d
Lx = P(x<d)
If right-censored/censored from above, value is at least u, but only
recorded as u.
Lx = Su
Common for policy limits!! Right censored is way more common.
3. Grouping Data special case of censoring
exact values
unknown Lx = Sa-
Sb
4. ALGEBRA REVIEW How can we simplify
(EXPONENTS):
L(α) =α4 /
240^α+1*100^α
1/
8
, SOA Exam Stam - MLE and Variance with all Correct &
100% Verified Answers| Latest Update| Already Graded A+
240^a+1*100^a
240^a*240^1*100^a
The constants dont attect the
likelihood, so 240^1 is not
necessary to keep in. We can
say the likelihood is
proportional without the
constant.
240^a*100^a
2/
8
