SOA EXAM STAM - MLE AND VARIANCE
MLE QUESTIONS AND ANSWERS
Truncated Data - Correct Answers -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)
Censored Data - Correct Answers -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.
Grouping Data - Correct Answers -special case of censoring
exact values unknown
Lx = Sa-Sb
ALGEBRA REVIEW (EXPONENTS):
L(α) =α^α+1*100^α
How can we simplify the likelihood
Hint- What can we do to the denominator?
Know your exponent rules!!!!
Look at Coaching Actuaries 2.1.5 on Section 2.1.2 - Correct Answers -240^a+1*100^a
240^a*240^1*100^a
The constants dont affect the likelihood, so 240^1 is not necessary to keep in. We can
say the likelihood is proportional without the constant.
MLE QUESTIONS AND ANSWERS
Truncated Data - Correct Answers -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)
Censored Data - Correct Answers -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.
Grouping Data - Correct Answers -special case of censoring
exact values unknown
Lx = Sa-Sb
ALGEBRA REVIEW (EXPONENTS):
L(α) =α^α+1*100^α
How can we simplify the likelihood
Hint- What can we do to the denominator?
Know your exponent rules!!!!
Look at Coaching Actuaries 2.1.5 on Section 2.1.2 - Correct Answers -240^a+1*100^a
240^a*240^1*100^a
The constants dont affect the likelihood, so 240^1 is not necessary to keep in. We can
say the likelihood is proportional without the constant.
