Hoover Index

Definition

For the purpose of measuring name, sector or geographic concentration, the Hoover Index is a simple index defined in terms of the absolute deviation from the mean (The $L^{1}$ norm).

Details

More precisely, if we have n exposures $E_{i}$ summing up to a total exposure of

$E_{T}=\sum _{i=1}^{n}E_{i}$

an average exposure

$E_{m}={\frac {E_{T}}{n}}$

and fractional exposures $w_{i}$ are defined as

$w_{i}={\frac {E_{i}}{E_{T}}}$

Then the Hoover index is defined as

$H={\frac {1}{2}}\sum _{i=1}^{n}|w_{i}-{\frac {E_{m}}{E_{T}}}|={\frac {1}{2}}\sum _{i=1}^{n}|w_{i}-{\frac {1}{n}}|$

Usage

None

Variations

None

Issues and Challenges

None

Implementation

Open Source implementations of the Hoover index are available in

• the Python library Concentration Library

See Also

None

References

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