mean_tightness_score

pymc_marketing.mmm.utility.mean_tightness_score(alpha=0.5, confidence_level=0.75)

Calculate the mean tightness score.

The mean tightness score is a risk metric that balances the mean return and the tail variability. It is calculated as:

\[Mean\ Tightness\ Score = \mu - \alpha \cdot Tail\ Distance\]

where:

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

• \(Tail\ Distance\) is the tail distance metric.

• \(\alpha\) is the risk tolerance parameter.

alpha (Risk Tolerance Parameter): This parameter controls the trade-off.

• Higher \(\alpha\) increases sensitivity to variability, making the metric value higher for spread dist

• Lower \(\alpha\) decreases sensitivity to variability, making the metric value lower for spread dist

Parameters:

alphafloat, optional

Risk tolerance parameter (default is 0.5).

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 mean tightness score given samples and budgets.