One of my clients recently asked me to modify an Excel model, so that the adoption of products entering the market would follow a S-curve. After some digging and googling, I came across this excellent post by Juan C. Mendez, where he proposes a clean and very practical way to use the logistic function, and calibrate it through 3 input parameters: the peak value, and the time at which the curve reaches 10% and 90% of its peak value.
The beauty of his approach is that his function is compact so it can be typed in easily in a worksheet cell, and the input very understandable. However, I found it a bit restrictive: transforming it for values other than 10% and 90% requires some recalibration, and more importantly, it cannot accomodate values that are not "symmetrical" around 50%.
So I set to work through a generalized solution to the following problem: find a S-Curve that fits any arbitrary value, rather than just 10% and 90%.
More...