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A pattern of a sequence is a sequence of integer indices with each indexdescribing the order of first occurrence of the respective symbol in theoriginal sequence. In a recent paper, tight general bounds on the block entropyof patterns of sequences generated by independent and identically distributed(i.i.d.) sources were derived. In this paper, precise approximations areprovided for the pattern block entropies for patterns of sequences generated byi.i.d. uniform and monotonic distributions, including distributions over theintegers, and the geometric distribution. Numerical bounds on the pattern blockentropies of these distributions are provided even for very short blocks. Tightbounds are obtained even for distributions that have infinite i.i.d. entropyrates. The approximations are obtained using general bounds and theirderivation techniques. Conditional index entropy is also studied fordistributions over smaller alphabets.

Patterns of i.i.d. Sequences and Their Entropy - Part II: Bounds for Some Distributions