Computes the r-th factorial moment of data or a distribution (mean of falling factorials)
FactorialMoment[data, r]
FactorialMoment[data, {r1, …, rm}]
FactorialMoment[dist, …]
FactorialMoment[r]
FactorialMoment[BinomialDistribution[n, p], 2]
→ -((1 - n)*n*p^2)FactorialMoment[{Subscript[k, 1], Subscript[k, 2], Subscript[k, 3]}, 3]
→ ((-2 + Subscript[k, 1])*(-1 + Subscript[k, 1])*Subscript[k, 1] + (-2 + Subscript[k, 2])*(-1 + Subscript[k, 2])*Subscript[k, 2] + (-2 + Subscript[k, 3])*(-1 + Subscript[k, 3])*Subscript[k, 3])/3FactorialMoment[{1, 2, 3, 4}, 1]
→ 5/2