By conventional wisdom, a feature that occurs too often or too rarely in a genome can indicate a functional element. To infer functionality from frequency, it is crucial to precisely characterize occurrences in randomly evolving DNA. We find that the frequency of oligonucleotides in a genomic sequence follows primarily a Pareto-lognormal distribution, which encapsulates lognormal and power-law ...

A lognormal interconnection length distribution function is derived from a large number of VLSI layouts. The assumption of a Weibull distribution could not be confirmed. Hierarchical slicing trees are derived from structural descriptions of the sample systems by recursive partitioning. Using the earlier proposed area estimation results, a new model for interconnection length estimation based on...

Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie gro...

This paper deals with the estimation of the lognormal-Pareto and the lognormal-Generalized Pareto distributions, for which a general result concerning asymptotic optimality of maximum likelihood estimation cannot be proved. We develop a method based on probability weighted moments, showing that it can be applied straightforwardly to the first distribution only. In the lognormal-Generalized Pare...