inverse_scaled_logistic_saturation

pymc_marketing.mmm.transformers.inverse_scaled_logistic_saturation(x, lam=0.5, eps=np.float64(1.0986122886681098))

Inverse scaled logistic saturation transformation.

It offers a more intuitive alternative to logistic_saturation, allowing for lambda to be interpreted as the half saturation point when using default value for eps.

\[f(x) = \frac{1 - e^{-x*\epsilon/\lambda}}{1 + e^{-x*\epsilon/\lambda}}\]

(Source code, png, hires.png, pdf)

Parameters:

xtensor

Input tensor.

lamfloat or array_like, optional, by default 0.5

Saturation parameter.

epsfloat or array_like, optional, by default ln(3)

Scaling parameter. ln(3) results in halfway saturation at lam

Returns:

tensor

Transformed tensor.