
Accession Number : ADA113866
Title : Moments of Particle Size Distributions under Sequential Breakage with Applications to Species Abundance.
Descriptive Note : Technical rept.,
Corporate Author : PRINCETON UNIV NJ DEPT OF STATISTICS
Personal Author(s) : Siegel,Andrew F ; Sugihara,George
PDF Url : ADA113866
Report Date : Nov 1981
Pagination or Media Count : 15
Abstract : The sequential broken stick model has appeared in numerous contexts, including biology, physics, engineering and geology. Kolmogorov showed that under appropriate conditions, sequential breakage processes often yield a lognormal distribution of particle sizes. Of particular interest to ecologists is the observed variance of the logarithms of the sizes, which characterizes the evenness of an assemblage of species. We derive the first two moments for the logarithms of the sizes in terms of the underlying distribution used to determine the successive breakages. In particular, for a process yielding n pieces, the expected sample variance behaves asymptotically as n log(n). These results also yield a new identity for moments of path lengths in random binary trees. (Author)
Descriptors : Biostatistics, Ecology, Distribution theory, Sequences(Mathematics), Analysis of variance, Asymptotic series, Paths, Length, Binary arithmetic, Random variables, Ecosystems, Mathematical models
Subject Categories : Biology
Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE