michaelis_menten#

pymc_marketing.mmm.transformers.michaelis_menten(x, alpha, lam)[source]#

Evaluate the Michaelis-Menten function for given values of x, alpha, and lambda.

\[\alpha \cdot \frac{x}{\lambda + x}\]

where:

\(x\): Channel spend.
\(\alpha\): Maximum contribution.
\(\lambda\) (k): The half-saturation point.

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

../../_images/pymc_marketing-mmm-transformers-michaelis_menten-1.png

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

../../_images/pymc_marketing-mmm-transformers-michaelis_menten-2_00_00.png

(png, hires.png, pdf)

../../_images/pymc_marketing-mmm-transformers-michaelis_menten-2_01_00.png

Parameters:

xfloat: The spent on a channel.
alphafloat: The saturation point. It represents the maximium number of customers that could be acquired through this channel at any point time. Must be non-negative.
lamfloat: The half-saturation point. Larger values represent less efficient channels.

Returns:

float: The value of the Michaelis-Menten function given the parameters.