f#
- pymc_marketing.bass.model.f(p, q, t)[source]#
Installed base fraction rate of change (adoption rate).
This function calculates the rate of new adoptions at time t as a proportion of the potential market. It represents the probability density function of adoption time.
- Parameters:
- p
floatorXTensorVariable Coefficient of innovation (external influence)
- q
floatorXTensorVariable Coefficient of imitation (internal influence)
- t
XTensorVariableor scalar Time points. An array carries no axis labels, so wrap it with
pymc.dims.as_xtensor()first.
- p
- Returns:
XTensorVariableThe adoption rate at each time point as a fraction of potential market
Notes
This is the derivative of F(t) with respect to time:
\[f(t) = \frac{(p+q)^2 \cdot e^{-(p+q)t}}{p \cdot (1+\frac{q}{p}e^{-(p+q)t})^2}\]Alternatively:
\[f(t) = (p + q \cdot F(t)) \cdot (1 - F(t))\]The peak adoption rate occurs at time \(t^* = \frac{\ln(q/p)}{p+q}\)