Statistical
HHI market concentration, Gini Impurity, and Shannon Entropy formulas
Quantify market concentration (HHI = SUM(s^2)*10000), classification Gini Impurity (1 - SUM(p^2)), and information Shannon Entropy in bits.
Three classic concentration & diversity metrics built from share vector p
Use nonnegative decimal shares that sum to one. For 0.5,0.3,0.2, the sum of squared shares is 0.38, giving HHI 3,800 and Gini impurity 0.62.
Shannon entropy in bits sums -p*LOG(p,2), with a zero-share term defined as zero. A negative share is invalid and must not be silently treated as zero.
Gini impurity describes class diversity; it is not the income-inequality Gini coefficient. HHI alone does not establish an antitrust conclusion, and no jurisdiction-specific threshold is assumed here.
The probability interpretation of Gini impurity uses two independent draws from the same distribution.
| Share Distribution p | HHI (0..10,000) | Gini Impurity | Shannon Entropy (Bits) |
|---|---|---|---|
| [50%, 30%, 20%] | 3,800 | 0.6200 | 1.4855 bits |
| [50%, 50%, 0%] (Even Coin) | 5,000 | 0.5000 | 1.0000 bit |
| [100%, 0%, 0%] (Pure / Monopoly) | 10,000 | 0.0000 | 0.0000 bits |
HHI, Gini Impurity, and Shannon Entropy formulas
Array squaring SUM(A2:A4 ^ 2) computes both HHI and Gini Impurity directly without helper columns.
=ROUND(SUM(A2:A4 ^ 2) * 10000, 0)Gini Impurity (1 - SUM(p^2)) and Shannon Entropy SUM(B2:B4)
Measures probability that two randomly drawn items belong to different classes.
=ROUND(1 - SUM(A2:A4 ^ 2), 4)Entropy in bits
Sum the helper terms in column B after validating the shares.
=ROUND(SUM(B2:B4),4)Try the example
Use the original values or change them to test your understanding.