If the instantaneous mortality rate for a species (or a group of humans) is 0.1/year, what is the mortality rate per month? Can you just divide $0.1/12$? This seems too simple and incorrect because mortality is an instantaneous rate.
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No, you can't, because the absolute number of people is not constant in the process. – Peter Jan 27 '15 at 17:20
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So how would you calculate monthly mortality rate? – user210990 Jan 27 '15 at 17:21
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Take the $12$ th root of $0,9$ and subtract it from $1$. – Peter Jan 27 '15 at 17:22
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The result is near the one we would get with the naive approach. – Peter Jan 27 '15 at 17:23
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So I followed these steps, but then I tested survival where $survival=\exp(mortality)$. My annual survival rate was $0.905$, so I'm looking for a monthly survival rate that will end up somewhere close to that. If I say that my monthly mortality is $mortality/12$ then my annual survival is $(\exp(mortality/12))^{12}=0.905$, while if I use a compound method then I get $0.900$. So it would appear as though the naive approach gives the correct answer. – user210990 Jan 27 '15 at 17:44
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I'm voting to close this question because it's very old with a good answer and needs no more attention. – Ethan Bolker Nov 18 '18 at 17:02
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There is actually another approach called Uniformly Distributions of Decrement, or UDD, and it assumes the same number of people would die in each year. It does precisely what you said: divide the annual q by 12 and it gives you monthly q. – DavidY Dec 14 '23 at 13:47
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Think of mortality like we think of compound interest: If I said that the effective annual rate of interest of an investment is $10\%$ per year, then what is the equivalent monthly rate of interest? That is to say, $$(1+j)^{12} = 1+i,$$ where $j$ is the monthly interest rate, and $i = 0.10$ is the effective annual rate. This gives us $$j = (1+i)^{1/12} - 1 = (1.1)^{1/12} - 1.$$ The force of mortality works in the same way.
heropup
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@TobyMak Yes, that was a typo. I will fix it, many thanks for catching it! – heropup Sep 14 '18 at 15:44
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For mortality (or any decrement), unlike interest rate, the formula should follow as-
j= 1- (1-i)^(1/12) where j = monthly decrement rate; i = annual mortality decrement rate.
N_P
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I agree this seems a change in presentation as we want to present mortality rate and force of mortality as a positive number. – DavidY Dec 14 '23 at 13:40