F

pymc_marketing.bass.model.F(p, q, t)

Installed base fraction (cumulative adoption proportion).

This function calculates the cumulative proportion of adopters at time t, representing the fraction of the potential market that has adopted the product.

Parameters:

pfloat or XTensorVariable

Coefficient of innovation (external influence)

qfloat or XTensorVariable

Coefficient of imitation (internal influence)

tXTensorVariable or scalar

Time points. An array carries no axis labels, so wrap it with pymc.dims.as_xtensor() first.

Returns:

XTensorVariable

The cumulative proportion of adopters at each time point

Notes

This is the solution to the Bass differential equation:

\[F(t) = \frac{1 - e^{-(p+q)t}}{1 + (\frac{q}{p})e^{-(p+q)t}}\]

When \(t=0\), \(F(t)=0\), and as \(t\) approaches infinity, \(F(t)\) approaches 1.