SOA EXAM STAM - MLE AND VARIANCE MLE || ANSWERED

SOA EXAM STAM - MLE AND VARIANCE
MLE || ANSWERED
Truncated Data - Correct Answer 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 Answer 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 Answer 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 Answer 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.

240^a*100^a
(240*100)^a

WHY DO WE MULTIPLY THE BASES AND NOT ADD THEM TO BE 340^a?