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Formula for S-Curves?
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. |
#2
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Formula for S-Curves?
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 "cardan" wrote in message oups.com... 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. |
#3
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Formula for S-Curves?
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 On Nov 13, 1:45 am, "Mike Middleton" wrote: 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 Middletonhttp://www.DecisionToolworks.com Decision Analysis Add-ins for Excel "cardan" wrote in message oups.com... 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. |
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