Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
10 will get you 20?
Replies:
9
Last Post:
Jan 25, 2014 5:37 PM




Re: 10 will get you 20?
Posted:
Jan 25, 2014 5:37 PM


On 01/25/2014 10:58 AM, JohnF wrote: > John <Man@the.keyboard> wrote: >> JohnF wrote: >>> Bart Goddard <goddardbe@netscape.net> wrote: >>>> JohnF wrote in news:lc00k7$k56$1@reader1.panix.com: >>>> >>>>> A tv news documentary touting the accomplishments of >>>>> some medical volunteer group in Afghanistan (sorry, >>>>> don't recall and failing to google exactly who) >>>>> stated that, "During the past 10 years life expectancy >>>>> has increased from 42 years to 62 years." >>>>> Just curious, and not particularly important, >>>>> but with what confidence can they make that >>>>> statement? In particular, imply that any such >>>>> measured change was caused by their efforts? >>>>> Firstly, I'm thinking it's kind of hard to >>>>> imagine observing that. Suppose they have the >>>>> normal (approximation to Poisson) distributions >>>>> for age at death for 2004,...,2013. So if the >>>>> mean u_2004 = 42, then what's happening in the >>>>> intervening years such that u_2014 = 62? >>>>> That is, how does the mean age at death increase >>>>> by 20 years in just 10 years (assuming indigenous >>>>> population only, e.g., no huge immigrant influx >>>>> of old people, etc)? >>>> >>>> Probably they have a statistic that says something >>>> like "If an infant makes it to age 1, then his >>>> life expectancy is 70 years." Then if they cut >>>> the infant mortalitiy rate in half (via better >>>> clinics and fewer bombings) they bring the average >>>> life expectancy up dramatically. >>> >>> Yes, that's exactly what happened, as per link in >>> preceding followup. >>> What this means, mathwise, is that numberofpeople >>> versus ageatdeath distribution has (at least) two peaks, >>> with an "extra" peak showing lots of people dying >>> before age 5. So the distribution isn't normal/poisson, >>> like I'd implicitly assumed. And that explains my question. >>> Then the math exercise question that I was kind of >>> asking, in the context suggested by the documentary, is >>> as follows. Suppose the distribution were normal. >>> Is there now any way you can introduce some public >>> health improvements, and after 10 years claim a life >>> expectancy improvement of 20 years? >> >> That's easy: >> 1: make everyone born after 2004 immortal apart from one weakness or >> "Achilles's Heel". >> 2: after 10 years, institute a policy of killing those who reach 62 >> years of age using that one weakness. > > Hmmm... have you seen the movie > http://wikipedia.org/wiki/Logan's_Run > That would work eventually, but I'm not sure the LE would > be 62 in 2014. That is, the >>measured<< LE wouldn't be 62 in 2014, > though in 2014 you could reliably predict it would eventually > become 62.
[...]
I wouldn't be suprized that they use mortality rates, say d_n is the estimated probability that someone who reaches the age n won't live to be n+1, for n = 0, 1, 2, ... 130. Those could be estimated from mortality trends for 2013, say. So, it wouln't follow a cohort over 70+ years (a group of people) ...
If P_0 is a "fictitious" cohort of 100,000 live births, all the same date and year, 1 year later there will be:
P_1 = P_0  P_0 d_0 people alive then 2 years later, P_2 = P_1  P_1 d_1 people alive [...]
P_{n+1} = P_n  P_n d_n people alive after exactly n+1 years.
The d_0 P_0 who die before age 1.0 are deemed to have lived 0.5 years on average.
The d_n P_n who die after age n exactly but before age n+1 exactly are deemed to have lived n+ 1/2 years on average.
So LE ~= [ sum_{n = 0 ... 130} d_n P_n * (n+ 1/2) ]/P_0 , with P_0 = 100,000 (live births ).
David Bernier
 http://www.bibliotecapleyades.net/sociopolitica/last_circle/1.htm



