We give a characterization of how fast the block length k may grow in order to have the relative frequence of occurrences of Blocks of length k among the first n tosses of a fair coin be 'good' approximations of their probabilities. The borderline will roughly be the logarithm of n with base 2,...

A characterization, extending a recent result due to Kotz and Steutel, is presented for exponential distributions. Links are made with other clearly related results, and multivariate analogues are considered.

Two stationary first-order autoregressive processes with Beta marginal distributions are presented. They are both linear, additive processes but the coefficients are Beta random variables. Their autocorrelation functions are investigated: one is positive and the other alternates in sign. The...