Some new exact distributions on coupon collector’s waiting time problems are given based on a generalized Pólya urn sampling. In particular, usual Pólya urn sampling generates an exchangeable random sequence. In this case, an alternative derivation of the distribution is also obtained from...

For a {0, 1}-pattern of finite length, an empirical process is introduced in order to describe the number of overlapping occurrences of the pattern at each level t[set membership, variant][0,1] in a sequence of the corresponding indicators of i.i.d. [0, 1]-valued observations of length n. A...

Let X1, X2,...,Xn be a time-homogeneous {0, 1}-valued Markov chain. Let Y = (Y1,...,Yr) denote the r-dimensional random vector, where Yi(i = l,...,r) represents the number of success runs of length ki(i = 1,...,r), k = (kl,...,kr). In this paper we obtain exact and recurrence formulae for the...