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.

Parámetros:

p : float o TensorVariablepython:float o TensorVariable

Coeficiente de innovación (influencia externa)

q : float o TensorVariablepython:float o TensorVariable

Coeficiente de imitación (influencia interna)

t : array_like o TensorVariablenumpy:array_like o TensorVariable

Puntos de tiempo

Devoluciones:

TensorVariable

The cumulative proportion of adopters at each time point

Notas

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.