Rate of Mortality in the Life Table

[Pacted]

First off, I apologise if this has been asked before (though I have failed to find any post addressing this).
My question essentially is: How is the force of mortality (Mu) in the Life Table constructed? And by this, I do not need the exact details, just conceptually speaking.

I notice that if I were to calculate Mu from the qx in the life table (by turning the q into p and using the [mu = -ln(p)]), I am making an assumption that the force of mortality is constant between the integer ages-- and as a result, my calculated value would differ from the given value of mu in the table.

Bonus question: What exactly is the correct usage of the different terminologies? (Rate vs force of mortality, initial vs central, etc.)

I am quite new to this subject, and I appreciate any advice! Thank you in advance!

Edit: I realise that I should have used the term 'Force' instead of 'Rate' in the post title, but I do not know how to edit it :/

 

[Robert Chadburn]

Hi Pacted
To answer your question with certainty, we would need to look at the source document (which is CMIR (Continuous Mortality Investigation Report) No 17), where it will say exactly what was done to get the rates and probabilities. I haven't done this (but feel free to do so yourself if you're interested).
In general, these days it would probably be most common to estimate the force of mortality at each age directly from the data, then work out q-type probabilities from these. Have you studied CT4 yet? In CT4 it explains how you would estimate mu at each age from data (number of deaths divided by exposed to risk), and then a mathematical formula would be fitted to represent the best model of mu-x over the age range. As this would be a continuous function of x, then we can read off mu-x at any age.
Then to get qx, say at integer ages, we could calculate 1-exp[ - integral of mu between ages x and x+1], along the lines that you suggest.
Note that this is something that you would not expect to examined on as such in CT5!
Robert

 

[Pacted]

Hi Pacted
To answer your question with certainty, we would need to look at the source document (which is CMIR (Continuous Mortality Investigation Report) No 17), where it will say exactly what was done to get the rates and probabilities. I haven't done this (but feel free to do so yourself if you're interested).
In general, these days it would probably be most common to estimate the force of mortality at each age directly from the data, then work out q-type probabilities from these. Have you studied CT4 yet? In CT4 it explains how you would estimate mu at each age from data (number of deaths divided by exposed to risk), and then a mathematical formula would be fitted to represent the best model of mu-x over the age range. As this would be a continuous function of x, then we can read off mu-x at any age.
Then to get qx, say at integer ages, we could calculate 1-exp[ - integral of mu between ages x and x+1], along the lines that you suggest.
Note that this is something that you would not expect to examined on as such in CT5!
Robert

Hello Robert,
Thank you for your reply.
Essentially, I can consider the mu given in the table as 'instantaneous', if I am understanding correctly?
I am in the middle of CT4 as well, and hopefully will get to the material mentioned soon!
Thanks again!

 

[Robert Chadburn]

Yes, so Mu at age 65 in the tables means the rate of mortality that's happening on the person's exact 65th birthday.