life expectancy (survivorship) math

Posted on 2002-07-18
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

Question by:omom

Expert Comment

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:

Hope it helps.

Accepted Solution

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:

Author Comment

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

Featured Post

Gigs: Get Your Project Delivered by an Expert

Select from freelancers specializing in everything from database administration to programming, who have proven themselves as experts in their field. Hire the best, collaborate easily, pay securely and get projects done right.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Artificial Intelligence comes in many forms, and for game developers, Path-Finding is an important ability for making an NPC (Non-Playable Character) maneuver through terrain.  A* is a particularly easy way to approach it.  I’ll start with the algor…
Performance in games development is paramount: every microsecond counts to be able to do everything in less than 33ms (aiming at 16ms). C# foreach statement is one of the worst performance killers, and here I explain why.
Microsoft Active Directory, the widely used IT infrastructure, is known for its high risk of credential theft. The best way to test your Active Directory’s vulnerabilities to pass-the-ticket, pass-the-hash, privilege escalation, and malware attacks …
A short tutorial showing how to set up an email signature in Outlook on the Web (previously known as OWA). For free email signatures designs, visit If you want to manage em…

776 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question