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Curtate expectation of life

K

Kristi

Member
Dear Tutors,

Could you please describe what the cutate expectation of life is used for. I am unsure of why we calculate it. (Ch 7 p 14)

Also, Chapter 10 page 45, (ii)(b)
"There are 3 deaths and the central exposed[PJC7] to risk....."
[PJC7]???

Thank you!
 
Hi Kristi,

Is your question just a subset of "Why do we bother with any of this nonsense?" ;-) If you accept the complete expectation of life as a worthwhile thing to calculate then I have an answer...

If we have a table of qx 's but don't have a formula for the mu x's then we can calculate the curtate one directly and use it to approximate the complete one by adding 0.5.

My more facetious answer is "because they ask you to do it in the exam!" :)

I don't really know what your other question is?? Sorry,

Cheers,
John
 
Hi,

I think what Kristi meant was the [PJC7] part in the sentence. We don't understand what [PJC7] stands for.

I'd also like to point out that in the same page (45 - chapter 10), The formula for the Poison likelihood should have been written as:

Given:
u = constant force of mortality
Central exposed to risk = 3.9 years

===> L = [(3.9*u)^3 * exp(-3.9*u)] / 3!
===> L = u^3 * exp(-3.9*u) * C (where C is a constant)


May I also please ask whether we can use the joint probability function (by independence) to work out the MLE of u:

Given:
TT = Product sign

L = TT(survivors) exp(-u(bi-ai)) x TT(deaths) u * exp(-u(ti-ai))

L = u^dx * exp(-3.9*u) (since the central exposed to risk is 3.9)


Many thanks.
 
Thanks, John. My question was aimed at why is it useful, which then helps me to remember how to calculate or derive something. Couldn't see its use given the complete expectation of life.

I don't expect you to be able to justify why we study any particular topic, moreover why I am studying!!!!!! ;)

Thanks again.
Kristi
 
Kristi,

There are probably other & better examples, but studying CT5 at the minute it's used when calculating benefits where a payout is made at the end of the year of death i.e. Curtate future lifetime + 1.

Hitme
 
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