There are 11 statistics on Skew partitions in the database:
(and possibly some waiting for verification)

St001435Skew partitions ⟶ ℤ
The number of missing boxes in the first row.
St001438Skew partitions ⟶ ℤ
The number of missing boxes of a skew partition.
St001487Skew partitions ⟶ ℤ
The number of inner corners of a skew partition.
St001488Skew partitions ⟶ ℤ
The number of corners of a skew partition.
St001490Skew partitions ⟶ ℤ
The number of connected components of a skew partition.
St001595Skew partitions ⟶ ℤ
The number of standard Young tableaux of the skew partition.
St001596Skew partitions ⟶ ℤ
The number of two-by-two squares inside a skew partition.
St001597Skew partitions ⟶ ℤ
The Frobenius rank of a skew partition.
St001614Skew partitions ⟶ ℤ
The cyclic permutation representation number of a skew partition.
St001658Skew partitions ⟶ ℤ
The total number of rook placements on a Ferrers board.
St001660Skew partitions ⟶ ℤ
The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board.