The remaining area of the convex hull of a Poisson process

Abstract: In Cabo and Groeneboom (1994) the remaining area of the left-lower convex hull of a Poisson point process with intensity one in the first quadrant of the plane was analyzed, using the methods of Groeneboom (1988), giving formulas for the expectation and variance of the remaining area for a finite interval of slopes of the boundary of the convex hull. However, the time inversion argument of Groeneboom (1988) was not correctly applied in Cabo and Groeneboom (1994), leading to an incorrect scaling constant for the variance. The purpose of this note is to show how the correct application of the time inversion argument gives the right expression, which is in accordance with results in Nagaev and Khamdamov (1991) and Buchta (2003).