By Cauchy–Schwarz inequality, the central moment functions satisfy μ μ n + m 2 ≤ ≤ μ μ 2 n μ μ 2 m . So, taking the limit, we have D n + m 2 ≤ ≤ ( 2 n ) ! ( 2 m ) ! ( n + m ) ! 2 D 2 n D 2 m . If some D 2 + n ≠ ≠ 0 for some n ≥ ≥ 1 , then D 2 D 2 + 2 n > 0 . In particular, D 2 + n , D 2 + 2 n , D 2 + 4 n , . . . > 0 . So the existence of any nonzero coefficient of order ≥ ≥ 3 implies the existence of nonzero coefficients of arbitrarily large order. Also, if D n ≠ ≠ 0 , then D 2 D 2 n − − 2 > 0 , D 4 D 2 n − − 4 > 0 , . . . . So the existence of any nonzero coefficient of order n implies all coefficients of order 2 , 4 , . . . , 2 n − − 2 are positive.