Actuarial Outpost MLE terminology
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 Short-Term Actuarial Math Old Exam C Forum

#1
10-13-2019, 01:20 PM
 Nasser SOA Join Date: Aug 2018 College: KFUPM Alumni Posts: 5
MLE terminology

Hi There,

are these two statements equivalent:

Domain
a - [2,3] =? b- 2 or 3

and both are discrete

I mean if I want to evaluate the MLE for a-[2,3]
p(x=2)+p(x=3) , b also has the same MLE?

Thanks
#2
10-13-2019, 03:23 PM
 gauchodelpaso Member SOA Join Date: Feb 2012 College: Eastern Michigan U Posts: 188

perhaps if you clarify the application, it may help me understand your question.

What's the context?

Normally we multiply the likelihoods for MLE, if independent.
__________________

German
______________
Prelims: 1/P - 2/FM - 3F/MFE - LTAM - STAM
VEE: Economics - Corporate Finance - Applied Statistics
#3
10-13-2019, 03:38 PM
 Nasser SOA Join Date: Aug 2018 College: KFUPM Alumni Posts: 5

Quote:
 Originally Posted by gauchodelpaso perhaps if you clarify the application, it may help me understand your question. What's the context? Normally we multiply the likelihoods for MLE, if independent.

claim counts
0 or 1
2
3 or more

each observation has two policies

find the maximum likelihood estimate- beta?
#4
10-13-2019, 05:13 PM
 gauchodelpaso Member SOA Join Date: Feb 2012 College: Eastern Michigan U Posts: 188

If I understand it correctly, you have 2 policies that may have 0 or 1 claim, 2 policies that have 2 claims each, and 2 policies that have 3 or more claims.

I would solve it as follows, but I may be wrong.

The likelihood would be
(pr(n=0)+pr(n=1))^2 * (pr(n=2))^2 * (pr(n>=3)^2
replace all betas and log it, derive respect to beta = 0.

If this is correct I get beta=2.71107
__________________

German
______________
Prelims: 1/P - 2/FM - 3F/MFE - LTAM - STAM
VEE: Economics - Corporate Finance - Applied Statistics

Last edited by gauchodelpaso; 10-13-2019 at 05:33 PM..
#5
10-13-2019, 11:09 PM
 Nasser SOA Join Date: Aug 2018 College: KFUPM Alumni Posts: 5

Thanks German, this how I would solve it
#6
10-14-2019, 01:40 AM
 gauchodelpaso Member SOA Join Date: Feb 2012 College: Eastern Michigan U Posts: 188

Quote:
 Originally Posted by Nasser Thanks German, this how I would solve it
you are welcome Nasser
__________________

German
______________
Prelims: 1/P - 2/FM - 3F/MFE - LTAM - STAM
VEE: Economics - Corporate Finance - Applied Statistics