> That is precisely equivalent to "additional years of survival at year n plus year n".
But that's (minus n) not what I suggested; it's not equivalent to the probability of living another ten years (say).
E.g. the life expectancy of five year olds (plus that they are five years old) is not sufficient information to determine how many of them (the probability one) will live to fifteen.
So ... "probability of surviving another 10 years" is different from life-expectency. It's a variant on mortality, though expressed over a 10 year period rather than a 1 year period.
For comparison, see the SSA's actuarial life tables. This gives 1-year mortality (both as percentage and as expected survivors per 100,000 lives) for each year of life from 0 to 119:
> What question are you trying to answer by looking at mortality probability?
Well, starting with the problem of 'life expectancy is biased by infant mortality', that it misleads people into thinking it was rare to live past 30 or whatever: stats like 'life expectancy at 20/30/etc.' are helpful.
I was just saying that I don't think 'life expectancy at x' when x is small is helpful, since in the limit we're back to where we started, and until x > end of relatively high risk, it suffers the same bias.
Looking at mortality probability would more directly show that early years are at risk, before it settles down and death is unlikely until old age. The old age curves (birth year is still the horizontal axis) would still show the truer change over time, but now so would the infant years.
You could even (/might need to) refine it to P{living another year} - P{having died within last year (or before)} or something.
But that's (minus n) not what I suggested; it's not equivalent to the probability of living another ten years (say).
E.g. the life expectancy of five year olds (plus that they are five years old) is not sufficient information to determine how many of them (the probability one) will live to fifteen.