<Tr> <Td> Pareto distribution </Td> <Td> (α k α x α + 1 x ≥ k 0 x <k (\ displaystyle (\ begin (cases) (\ frac (\ alpha k ^ (\ alpha)) (x ^ (\ alpha + 1))) &x \ geq k \ \ 0&x <k \ end (cases))) </Td> <Td> (1 0 <α <1 1 2 α − 1 α ≥ 1 (\ displaystyle (\ begin (cases) 1&0 <\ alpha <1 \ \ (\ frac (1) (2 \ alpha - 1)) & \ alpha \ geq 1 \ end (cases))) </Td> </Tr> <Tr> <Td> Chi - squared distribution </Td> <Td> 2 − k / 2 e − x / 2 x k / 2 − 1 Γ (k / 2) (\ displaystyle (\ frac (2 ^ (- k / 2) e ^ (- x / 2) x ^ (k / 2 - 1)) (\ Gamma (k / 2)))) </Td> <Td> 2 Γ (1 + k 2) k Γ (k / 2) π (\ displaystyle (\ frac (2 \, \ Gamma \ left ((\ frac (1 + k) (2)) \ right)) (k \, \ Gamma (k / 2) (\ sqrt (\ pi))))) </Td> </Tr> <Tr> <Td> Gamma distribution </Td> <Td> e − x / θ x k − 1 θ − k Γ (k) (\ displaystyle (\ frac (e ^ (- x / \ theta) x ^ (k - 1) \ theta ^ (- k)) (\ Gamma (k)))) </Td> <Td> Γ (2 k + 1 2) k Γ (k) π (\ displaystyle (\ frac (\ Gamma \ left ((\ frac (2k + 1) (2)) \ right)) (k \, \ Gamma (k) (\ sqrt (\ pi))))) </Td> </Tr> <Tr> <Td> Weibull distribution </Td> <Td> k λ (x λ) k − 1 e − (x / λ) k (\ displaystyle (\ frac (k) (\ lambda)) \, \ left ((\ frac (x) (\ lambda)) \ right) ^ (k - 1) e ^ (- (x / \ lambda) ^ (k))) </Td> <Td> 1 − 2 − 1 / k (\ displaystyle 1 - 2 ^ (- 1 / k)) </Td> </Tr>

Which of the following gini ratios indicates the lowest degree of income inequality