Formula for S-Curves?

[cardan]

Hello All,

I am trying to figure out a formula that will spread out a certain
number (costs) among a predefined number of periods (months) into an S-
curve shape.

Essentially, I have 3 inputs.
1. Cost,
2. Start Date(month/year) and
3. Duration (months).

The "cost" will start in the beginning month and will be spread over
the total.

The curve does not have to be too precise, since there are a few
variations out there. Is there something out there that is a simple
formula?

Any feedback, advice, or direction would be greatly appreciated.
Thank you for your time in advance.

 

[Mike Middleton]

cardan or carlsondaniel -

(1) You might get an acceptable curve by entering eyeball-estimated data on
a worksheet, creating an XY (Scatter) chart, and using Insert Trendline for
a polynomial of order 3. But it might curve in the "wrong" direction at the
extremes.

(2) A usually "nicer" fit uses the logistic function to get a monotonic
S-shaped curve, but it'll require using Solver to find the coefficients for
the logistic function. If you need this approach, use google or post back.

- Mike Middleton
http://www.DecisionToolworks.com
Decision Analysis Add-ins for Excel

 

[SteveM]

Do a google search on the Pearl Curve and Gompertz Curve. If you are
near a library, see Wayne Winston's book "Financial Models Using
Simulation and Optimization." He shows you how to do it explicitly.

SteveM