Does anyone know of a short explanation why it is that when we calculate the deaths per exposure for exact exposure we obtain q from 1-e^-hz (seemingly from the use of the AN extimator but no source says so outright), but when we figure out the same ratio for actuarial exposures we are not finding the hazard rate (taking exponentiating (to get Sx) then getting q= 1-Sx)?
In other words, for exact exposures we have q = 1 - e^-d/e. For actuarial exposures we have q = (n) d/e.
We determine deaths per exposure units for both. But why is one the hazard rate and the other "q". Seems to me that they both should be the either the hazard rate or q since the only thing that is different between them is the number of months given to exposure of someone dies (to the end of the year). I can't see a difference in my ASM manual. I found another souce online (BPP) with a discussion about it but it says "it can be shown...." so it is not helpful.
Suppose I could memorize when to use each but I though someone would understand the reason why finding q is different based on how exposure for a death is counted.
Thanks.
In other words, for exact exposures we have q = 1 - e^-d/e. For actuarial exposures we have q = (n) d/e.
We determine deaths per exposure units for both. But why is one the hazard rate and the other "q". Seems to me that they both should be the either the hazard rate or q since the only thing that is different between them is the number of months given to exposure of someone dies (to the end of the year). I can't see a difference in my ASM manual. I found another souce online (BPP) with a discussion about it but it says "it can be shown...." so it is not helpful.
Suppose I could memorize when to use each but I though someone would understand the reason why finding q is different based on how exposure for a death is counted.
Thanks.
exact vs actuarial exposures