forget that.... too much coffee On Monday, February 16, 2015, Thane Plambeck <tplambeck@gmail.com> wrote:
also i think it might have switched to 1/2 at age 100.
On Monday, February 16, 2015, Thane Plambeck <tplambeck@gmail.com <javascript:_e(%7B%7D,'cvml','tplambeck@gmail.com');>> wrote:
actuarial tables used in life insurance seem to reflect the stoppage (i recall). i remember that a fixed probability of 1/6 of living another year at all ages 95 and above was used in one life insurance (or maybe annuity) quotation i was given long ago. there was probably more cold-hearted approximation than actual scientific investigation involved in these numbers though
On Monday, February 16, 2015, Warren D Smith <warren.wds@gmail.com> wrote:
It seems the stoppage of exponential growth in death rate with age (the "end" of Gompertz's law) at about age 100 has been noticed before. Furthermore, it has been disputed. Apparently the dispute is based on the claim that the ages of very old people are commonly misreported. Even if the misreporting is a random both-signed perturbation with zero mean, that still will cause the illusion of an "end of Gompertz's law." Some authors claim Gompertz really continues to work out to the oldest ages in both humans and other species. Others claim: that may depend on which species. Apparently some species do exist in which Gompertz-stoppage really does occur (invertebrates like fruit flies especially) and some exist in which it seems to keep working (mice). Deciding who is right is not easy for me.
The stoppage (if genuine) could be "explained" by the following modification of my silly "challenges/answers" model. Imagine there are two kinds of answers, durable ones and non-durable ones. They get obliterated each year (or day, or whatever) with two fixed small probabilities -- the durable ones with a smaller probability of obliteration, but durable answers are initially rare. Each year (or day, or whatever) you are "challenged" and if you still have the "answer" to the challenge you are allowed to live. This model predicts the exponential death rate increase, but eventually the non-durable answers have been thinned so much that the durable ones outmass them. That causes a switchover to a slower Gompertzian growth constant in the exponential.
It seems to me reasonable that such a thing ought to happen: if you accepted the challenges/answers model in the first place, then you should accept that some answers must be more durable, whereupon automatically you are logically forced to predict this. If the transition really does not exist in humans then I'll just slither out of that by claiming the constants in my picture are such that we don't see it; I have no trouble fitting reality either way.
Re Infant mortality (defined as deaths of babies <1 year old) the worst place to be a baby is Washington DC and the best is Massachusetts (in the USA)... in 2009 USA there were 4.18 deaths per 1000 in the first 28 days of life ("neonatal"; 28 days is 1/13 years), and 2.21 in the rest of the first year, showing the death rate is 22.7 times greater during the neonatal period. Further, in the "early neonatal" period (first 25% of it) there were 3.23 deaths/1000 in year 2010, versus 0.82 in the rest of the neonatal period. This is 15.7 times greater death rate. So there initially is a very severe decline in death rate. It's almost like a 1/age^2 power law singularity, except that formula would yield infinite integral so cannot be correct...
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
-- Thane Plambeck tplambeck@gmail.com <javascript:_e(%7B%7D,'cvml','tplambeck@gmail.com');> http://counterwave.com/
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/