Death probability in time interval I have the following question
Given the anual death rate $r$ for a group of persons (units of deaths per $1,000$ individuals per year), what is the probability that any given individual will die within the next $x$ months? This is assuming that death is an IID event, and of course, which can only happen once.
My problem is that I haven't been able to identify which probability distribution to use, nor which are the parameters given for such distribution. I'd really appreciate your help :)
 A: Deaths in the next $x$ months are distributed as $D\sim Po\left(\frac {rx}{12}\right)$, so the probability there is exactly $1$ death in this time ($D=1$) is $\frac{rx}{12}e^{-rx/12}$, the probability that there is at least $1$ death ($D\geq1$) is $$1-e^{-rx/12}$$
This agrees with Graham Kemp's answer, with just the rate being slightly different. Also notice that $r$ has "units" of deaths per $1000$ individuals per year, so there is no need to factor in the $10^{-3}$. The "per year" part is corrected by the inclusion of $\frac x{12}$.
A: You want the distribution for the time until an occurance of an event which may occur at a constant average rate of $10^{-3}\mathrm{yr}^{-1}$, in independent increments over time.
This is an exponential distribution, whose cumulative distribution function for $t$ (measured in years) is:  $$\mathsf P(X\leq t) ~=~ 1-e^{-t /1000}$$
A: In your question, I understand that you are looking for a model to characterize the length between consecutive events to determine a death probability in given time interval. However, you might want to consider looking at the the Poisson distribution as a death model to characterize the number of deaths in a given time interval.
For example, the classic Poisson example is the data set of von Bortkiewicz (1898), for the chance of a Prussian cavalryman being killed by the kick of a horse. Ten army corps were observed over 20 years, giving a total of 200 observations of one corps for a one year period. The period or module of observation is thus one year. The total deaths from horse kicks were 122, and the average number of deaths per year per corps was thus $\lambda = 122/200 = 0.61$. 
It can be seen that the Poisson distribution gives a close fit for the actual Prussian data, where $\lambda = 0.61$ is the average number expected per year for the whole sample, and the successive terms of the Poisson formula are the successive probabilities. The Poisson distribution is given as
$$p(k) = e^{-\lambda}\frac{\lambda^k}{k!}$$
Given that probability, then over the 200 years observed we should expect to find a total of 108.68 = 109 years with zero deaths. It turns out that 109 is exactly the number of years in which the Prussian data recorded no deaths from horse kicks. 
For the entire set of Prussian data, where $p$ = the predicted Poisson frequency for a given number of deaths per year, $E$ is the corresponding number of years in which that number of deaths is expected to occur in our 200 samples (that is, our p value times 200), and $A$ is the actual number of years in which that many deaths were observed, we have:

and the match seems very good throughout. 
