Actuarial Outpost > Life Conversion of monthly mortality table
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#1
11-11-2018, 10:18 PM
 EK56 SOA Join Date: Feb 2013 Posts: 9
Conversion of monthly mortality table

Hello,

I have a mortality table where the q's are given in months. I have to convert that mortality table to one where the q's are in years. So, for a given year "aaaa" I took the average of the 12 q's in the year "aaaa" as my yearly q's.

q(aaaa) = [q(January of aaaa) + q(February of aaaa) + … + q(December of aaaa)] / 12

Is this correct?

Gracias y Saludos
EK56
#2
11-11-2018, 10:53 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,999

Where do your q values come from? Are they deaths per month? If so, averaging them will get you the average deaths per month, not deaths per year which is what you want.

Try making a life table from the q values that you have and then computing the annual q from the life table (dx/lx).

Remember, you can pick any radix (initial value for l) that you want, so chose an easy one (like 12,000,000)
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#3
11-11-2018, 11:00 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,039

It would be easier to answer if I understood why the original table existed and why someone wanted you to convert it. Without that knowledge, I can only suggest that you make sure that the q’s in the table are annual rates applicable during the stated months. If the q’s in the table are monthly rates, it probably makes more sense to just add them up to get an annual death rate rather than to average them.

ETA: ninja’d
#4
11-12-2018, 10:22 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,039

Quote:
 Originally Posted by Colymbosathon ecplecticos Where do your q values come from? Are they deaths per month? If so, averaging them will get you the average deaths per month, not deaths per year which is what you want. Try making a life table from the q values that you have and then computing the annual q from the life table (dx/lx).
The life table approach works only (or at least, best) if you can assign the q’s in the table to month of age, which is not suggested to me from the limited description. From the description, I think it contains q’s by calendar month (of observation? Empirical q’s?).