<P> c assumes its minimum value of zero for complete equality (all x are equal). Its most notable drawback is that it is not bounded from above, so it cannot be normalized to be within a fixed range (e.g. like the Gini coefficient which is constrained to be between 0 and 1). It is, however, more mathematically tractable than the Gini Coefficient . </P> <P> Provided that negative and small positive values of the sample mean occur with negligible frequency, the probability distribution of the coefficient of variation for a sample of size n has been shown by Hendricks and Robey to be </P> <Dl> <Dd> d F c v = 2 π 1 / 2 Γ (n − 1 2) e − n 2 (σ μ) 2 c v 2 1 + c v 2 c v n − 2 (1 + c v 2) n / 2 ∑ ∑ ′ i = 0 n − 1 ⁡ (n − 1)! Γ (n − i 2) (n − 1 − i)! i! n i / 2 2 i / 2 (σ μ) i 1 (1 + c v 2) i / 2 d c v, (\ displaystyle \ mathrm (d) F_ (c_ (\ rm (v))) = (\ frac (2) (\ pi ^ (1 / 2) \ Gamma \ left ((\ frac (n - 1) (2)) \ right))) \; \ mathrm (e) ^ (- (\ frac (n) (2 \ left ((\ frac (\ sigma) (\ mu)) \ right) ^ (2))) (\ frac ((c_ (\ rm (v))) ^ (2)) (1 + (c_ (\ rm (v))) ^ (2)))) (\ frac ((c_ (\ rm (v))) ^ (n - 2)) ((1 + (c_ (\ rm (v))) ^ (2)) ^ (n / 2))) \ sideset () (^ (\ prime)) \ sum _ (i = 0) ^ (n - 1) (\ frac ((n - 1)! \, \ Gamma \ left ((\ frac (n-i) (2)) \ right)) ((n - 1 - i)! \, i! \,)) (\ frac (n ^ (i / 2)) (2 ^ (i / 2) \ left ((\ frac (\ sigma) (\ mu)) \ right) ^ (i))) (\ frac (1) ((1 + (c_ (\ rm (v))) ^ (2)) ^ (i / 2))) \, \ mathrm (d) c_ (\ rm (v)),) </Dd> </Dl> <Dd> d F c v = 2 π 1 / 2 Γ (n − 1 2) e − n 2 (σ μ) 2 c v 2 1 + c v 2 c v n − 2 (1 + c v 2) n / 2 ∑ ∑ ′ i = 0 n − 1 ⁡ (n − 1)! Γ (n − i 2) (n − 1 − i)! i! n i / 2 2 i / 2 (σ μ) i 1 (1 + c v 2) i / 2 d c v, (\ displaystyle \ mathrm (d) F_ (c_ (\ rm (v))) = (\ frac (2) (\ pi ^ (1 / 2) \ Gamma \ left ((\ frac (n - 1) (2)) \ right))) \; \ mathrm (e) ^ (- (\ frac (n) (2 \ left ((\ frac (\ sigma) (\ mu)) \ right) ^ (2))) (\ frac ((c_ (\ rm (v))) ^ (2)) (1 + (c_ (\ rm (v))) ^ (2)))) (\ frac ((c_ (\ rm (v))) ^ (n - 2)) ((1 + (c_ (\ rm (v))) ^ (2)) ^ (n / 2))) \ sideset () (^ (\ prime)) \ sum _ (i = 0) ^ (n - 1) (\ frac ((n - 1)! \, \ Gamma \ left ((\ frac (n-i) (2)) \ right)) ((n - 1 - i)! \, i! \,)) (\ frac (n ^ (i / 2)) (2 ^ (i / 2) \ left ((\ frac (\ sigma) (\ mu)) \ right) ^ (i))) (\ frac (1) ((1 + (c_ (\ rm (v))) ^ (2)) ^ (i / 2))) \, \ mathrm (d) c_ (\ rm (v)),) </Dd>

Can you have a coefficient of variation greater than 100