Say life expectancy at age X is Y further years, and life expectancy at age (X + Y) is Z further years. I think at least part of the reason why Z isn’t 0 is that if you’re following someone along their life, the fact that they lived Y further years is more evidence to update on. If X means “lived to at least X years”, then P(X+Y+Z|X+Y) > P(X+Y+Z|X), because living to X+Y years indicates certain things about, say, your health, genetics, etc that aren’t indicated by just living to X years.
Yes indeed. Though the curiosity remains that at the time of death, that evidence is woefully wrong, because you’re the least healthy person alive; an extreme outlier. Which means, life expectancy tables are only useful if you’re not actually near death. Their % prediction error approaches infinity as you approach death (and the error is systematically in one direction).
Maybe this is obvious, but:
Say life expectancy at age X is Y further years, and life expectancy at age (X + Y) is Z further years. I think at least part of the reason why Z isn’t 0 is that if you’re following someone along their life, the fact that they lived Y further years is more evidence to update on. If X means “lived to at least X years”, then P(X+Y+Z|X+Y) > P(X+Y+Z|X), because living to X+Y years indicates certain things about, say, your health, genetics, etc that aren’t indicated by just living to X years.
Yes indeed. Though the curiosity remains that at the time of death, that evidence is woefully wrong, because you’re the least healthy person alive; an extreme outlier. Which means, life expectancy tables are only useful if you’re not actually near death. Their % prediction error approaches infinity as you approach death (and the error is systematically in one direction).