Example

Costs have, unfortunately, no limit. Such a limit is needed for a meaningful example for the Logistic function. A commonly used example are sales. A new product might be sold until the potential market is saturated.

The number of sales per month is modelled using the Logistic function and the parameters listed below. Then, a bit of noise was added.

Parameter for Optimizing the fit to the Logistic function

The parameter used for the modeling is always the top one of the tripples below. The subsequent parameter are the lower (_L) and upper (_U) bounds for the optimization.

- MaximumMarketSize_M = 1000
- MaximumMarketSize_M_L = 500
- MaximumMarketSize_M_U = 2000

- Steepness_s = 0.5
- Steepness_s_L = 0
- Steepness_s_U = 1

- Offset_cX = 6.83
- Offset_cX_L = 0
- Offset_cX_U = 16

- Offset_cY = 100
- Offset_cY_L = 20
- Offset_cY_U = 180

The modelled sales data (using a Logistic function) were fitted by the Logistic function and unsurprisingly show a good fit to the fit.