Asymptotic analysis usually involves complex analysis or probability theory or both. The idea is to get a handle on the behavior of the number of compositions or words of interest, or of a statistic on these objects as n →∞. Applying results from complex analysis we can obtain growth rates for the statistics of interest. On the other hand, when considering compositions as randomly selected from all compositions (that is, all compositions of n are equally likely to occur), we can derive results on the average or variance of a statistic, which now is a random variable.