Question 4 Septemper 2009 CT4 Exam

Why may i ask does the question ask for an expression estimate of mu_x, and the solution gives an expression which is mu hat x, which is actually estimating mu_x+1/2 given the rate interval specified.

Since the question specifically states mu_x, with no hat,to answer this question correctly wouldn't you need to commit the mortal sin of adjusting the deaths data and the exposed to risk also into the "age nearest birthday" format so it cuts the middle of the rate interval.

 

CT4 April 2005 Question B6

Seems to have the same issue in (ii)?

 

bumpp

 

Hello DevonMathews

I agree with the examiners report. Let me explain why.

Deaths' Data
We are looking at people aged x last birthday. This may be a person who has just turned x or is just about to turn x+1. This means that we actually have a group of people aged between ages x and x+1. Asumming uniform distribution of deaths we are actually estimating the rate for age x+1/2.

Model
For these things I seem to remember that if u found yourself with a mu then u must realise that the underlying model is the Poisson, if q then Binomial. By the nature of the poisson model u are actually estimating the rate at the middle over the year x- x+1 as defined by the deaths' data in our question (the year in question depends on the deaths' data). So again it should be for age x+1/2.

The Question
The question has asked for mu_x. This is normally in relation to the fact that the death data refers to last birthday x. This does not mean that you should adjust the data. U should be finding rates as the deaths data indicates. I would not be surprised it is part of the question to actually see that the deaths' data recorded actually gives rates for x+1/2 not x. The deaths' data is given such that u are actually finding mu_x+1/2. It is indeed an actuarial sin to adjust death data unless specifically asked to do so. I haven't seen it done before.


I hope this clarifies your question. The same applies for the 2005 question.

All the best.

 

BUMP

Hi, could someone else (maybe one of the knowledgeable mods?? ) have a look at this question please?

The answer that is given below seems to imply we should go against what we've been taught and what, to my mind is wrong, because the data dictates this?

Is that right?? Confusing somewhat and a bit unfair, if that was in my exam, I'll be thinking, do I seriously right down an incorrect result or have I missed something? Queue rest of the exam wondering what I've missed...

 

Hi,

Just wondering if anyone would share my line of reasoning on this question.

Consider an individual born in the calendar year 1990. On population census date, 30 June 2005, he is aged 15 last birthday given that he was born between 1 January and 30 June. So that on 1 January 2005, he is aged 15 neareast birthday.
If however, he was born between 1 July and 31 December, on population census date 30 June 2005, he will be aged 14 last birthday. So that on 1 January 2005, he is aged 14 nearest birthday.
Then we can say that, the number of lives aged x last birthday on any population census date, 30 June 2005 say, is also aged x nearest birthday on the 1 January of that population census date i.e. 1 January 2005 in this example.
Now, having population data on the 1 January of the years, we can invoke the principle of correspondence and convert the nearest to last in the usual way.

I reckon this is more ideal than assuming a linear population between census dates.

What d'yall think?
N.B. I have noticed recently, that my posts take a while to show. Is this a development?