  In this paper, we study concave compositions, an extension of partitions that
were considered by Andrews, Rhoades, and Zwegers. They presented several open
problems regarding the statistical structure of concave compositions including
the distribution of the perimeter and tilt, the number of summands, and the
shape of the graph of a typical concave composition. We present solutions to
these problems by applying Fristedt's conditioning device on the uniform
measure.
