  Bj\"orner and Wachs defined a major index for labeled plane forests and
showed that it has the same distribution as the number of inversions. We define
and study the distributions of a few other natural statistics on labeled
forests. Specifically, we introduce the notions of bottom-to-top maxima, cyclic
bottom-to-top maxima, sorting index, and cycle minima. Then we show that the
pairs (inv, Bt-max), (sor, Cyc), and (maj, Cbt-max) are equidistributed. Our
results extend the result of Bj\"orner and Wachs and generalize results for
permutations. We also introduce analogous statistics for signed labeled forests
and show equidistribution results which generalize results for signed
permutations.
