The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process describing simple replicative systems. The shape of the resulting distribution, about which little has been known, is found essentially indistinguishable from...

We characterize all stationary time reversible Markov processes whose finite dimensional marginal distributions (of all orders) are infinitely divisible– MISTI processes, for short. Aside from two degenerate cases (iid and constant), in both discrete and continuous time every such process with full support is a branching process with Poisson or Negative Binomial marginal univariate distribution...

This paper has two main objectives. First, it develops the multifractal formalism in a context suitable for both, measures and functions, deterministic as well as random, thereby emphasizing an intuitive approach. Second, it carefully discusses several examples, such as the binomial cascades and self-similar processes with a special eye on the use of wavelets. Particular attention is given to a...

We implement and prove correct binomial heaps and skew binomial heaps. Both are data-structures for priority queues. While binomial heaps have logarithmic findMin, deleteMin, insert, and meld operations, skew binomial heaps have constant time findMin, insert, and meld operations, and only the deleteMin-operation is logarithmic. This is achieved by using skew links to avoid cascading linking on ...

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