• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

census data questions

S

swati

Member
Hi, I am having difficulty understanding questions pertaining to census data
Please guide
 
Hi Mr. Potter,

In connection with problems on exposed to risk, would you pls explain how to proceed when census and death data have different age definitions?
That's where I get most muddled :(

Thanks!
V S R
 
Hello Mr Potter,
I have difficulty in in linking census data and death data when they have two different definitions. I would like to quote a sum here which appeared in one of our Indian CT4 paper.

A mortality investigation was held between 1.1.2007 and 1.1.2009.The following information was collected .The figures in the table below are the numbers of lives on each census date with specified age labels

Date
Age last birthday 1.1.2007 1.1.2008 1.1.2009
48 3486 3384 3420
49 3450 3507 3435
50 3510 3595 3540
During the investigation there were 42 deaths at age 49 nearest birthday.Estimate mu(49) stating any assumptions you make.

Thanks and regards,
Swati
 
Hi Swati,

Here, mu(49) = Theta(49) / E49c = 42 / E49c

We have to make the denominator correspond to the numerator. This is the PRINCIPLE OF CORRESPONDENCE.

Here, theta*(49) = number of DEATHS aged 49 nearest BDay
I invent P* so that it corresponds with the definition of Theta(49):
P*(49,t) = number of PEOPLE aged 49 nearest BDay at time t

This bit is easy, you just copy and write "people" instead of "deaths".

Now, E49c = integral t = 0 to 2 of P*(49,t)

which we approximate using trapezium rule as 0.5 P*(49,0) + P*(49,1) + 0.5 P*(49,2)

All that remains is to approximate P*(49,t) (the data we want) from P(49,t) (the data we have)

P*(49,t) = number of PEOPLE aged 49 nearest BDay
P(x,t) = number of PEOPLE aged 49 last BDay

The people aged 49 nearest birthday will be between the ages of 48.5 and 49.5. So, half of them are 48 on their last birthday and half of them are 49 on their last birthday:

P*(49,t) = 0.5 {P(48,t) + P(49,t)}

Copy this in for t = 0,1 2 above:

E49c = 0.5*0.5{P(48,0) + P(49,0)} + 0.5{P(48,1) + P(49,1)}
+ 0.5*0.5 {P(48,2) + P(49,2)}

= 0.5*0.5{3486 + 3450} + 0.5{3384 + 3507}
+ 0.5*0.5 { 3420 + 3435}
= 6893.25

So, mu(49) = 42 / 6893.25 = 0.0060929

Check my numbers but I hope this is the answer.

Good luck!
John
 
Last edited:
Back
Top