tail_distance

pymc_marketing.mmm.utility.tail_distance(confidence_level=0.75)

Calculate the absolute distance between the mean and the quantiles.

It is a simple and interpretable metric that can be used to assess the risk.

The tail distance is calculated as:

\[\begin{split}Tail\\ Distance = |Q_{(1 - \\alpha)} - \\mu| + |\\mu - Q_{\\alpha}|\end{split}\]

where:

• \(\\mu\) is the mean of the sample returns.

• \(Q_{(1 - \\alpha)}\) is the quantile at the specified confidence level.

• \(Q_{\\alpha}\) is the quantile at the specified confidence level.

Parameters:

confidence_levelfloat, optional

Confidence level for the quantiles (default is 0.75). Confidence level must be between 0 and 1.

Returns:

UtilityFunctionType

A function that calculates the tail distance metric given samples and budgets.