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life expectancy (survivorship) math

Posted on 2002-07-18
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Last Modified: 2013-12-26
I need an function for crude life expectancy (that is a life expectancy based solely on genetics, no environmental considerations)

I would expect a curve of this equation to look like a gauss/normal distrubution weighted to the right of the median. Kinda like this:

|
|                            *
|                        *         *
|                     *              *
|                  *                   *
|               *                        *
|          *                               *
|       *                                    *
| *                                            *
___________________________________________


A logarithmic normal distribution is close, but it looks like a guass/normal distrubution weighted to the right of the median.

|
|            *
|        *        *
|      *             *
|     *                 *
|    *                      *
|   *                          *
|  *                              *
| *                                    *
___________________________________________

x is age (in years)
y is # of lifeforms


---------------------------------
maybe this

x   = age interval (often implicitly an interval)  -this can be a month, year
Nx = survivors beginning at age interval x
lx   = proportion of orgs surviving to start of x
dx  = organisms dying between x and x+1

Derive subsequent columns from the data of x and Nx
dx = Nx+1 - Nx
lx = Nx / No

ex = the sum of all Lx from age x to the last age / N of age x

Lx = (Nx + Nx+1) / 2



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Question by:omom
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3 Comments
 
LVL 2

Expert Comment

by:macgre
ID: 7188576
What you ask for is non-trivial but I suggest working in reverse.  First decide what sort of curve you want then work your varibales from that.  Skewed curve probabilites can be calculated using Binomial Distrubutions, but when the population is large enough (as in your case) then normalized approximations can be used.

Try this link for more info:
http://online.moraine.cc.il.us/Summer/2002/MTH139-303/lesson17.htm

Hope it helps.
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LVL 6

Accepted Solution

by:
GnarOlak earned 100 total points
ID: 7188645
I found some links related to a set of distributions that resemble what you posted.  I have included a few of the links.  You can also try the following entries in your favorite search engine.  Hope this helps.

For searching:
"gumbel distribution"
"fisher tippett distribution"

A few links:
http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm
http://www.xycoon.com/gumbel.htm
http://mathworld.wolfram.com/Fisher-TippettDistribution.html
http://ic.net/~jnbohr/java/CdfDemoArgs.html
0
 

Author Comment

by:omom
ID: 7189042
I think the gumbel distribution is what i'm looking for
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