The largest missing value in a composition of an integer

In this paper we find, asymptotically, the mean and variance for the largest missing value (part size) in a composition of an integer nn. We go on to show that the probability that the largest missing value and the largest part of a composition differ by one is relatively high and we find the mean for the average largest value in compositions that have this property. The average largest value of compositions with at least one non-zero missing value is also found, and used to calculate how many distinct values exceed the largest missing value on average.