While simulations are something I want to get into in the future, I don't think I'm knowledgeable enough on survival analysis to answer your question. With that said, what you're looking at sounds to me to be a survival analysis. Each person is born with, say, an expected useful life. If a population averages a life of 80 years 99% of the time, then we should expect to see strong clustering around 80 for their deaths. What you're trying to do, however, is to analyze this on a day-by-day or year-by-year basis. This is where I'm foggy. How much can we say a person's yearly life contributes to their meeting their expected death rate of the population to which they belong? I wouldn't think it is a forgetful process such that each year is independent of the previous. It would then be a continuous conditional probability, such that we want to know
This probability should increase each year toward a high probability around that expected death rate. I'm sure if you do some research into survival analysis, you'll find the sort of functions that can help you process this. In particular, check out the hazard function.