For more than a century, microbiologists have sought to determine the species richness of bacteria in soil, but the extreme complexity and unknown structure of soil microbial communities have obscured the answer. We developed a statistical model that makes the problem of estimating richness statistically accessible by evaluating the characteristics of samples drawn from simulated communities wi...

We examine the evolution of the IGM Lyα optical depth distribution using the transmitted flux probability distribution function (PDF) in a sample of 63 QSOs spanning absorption redshifts 1.7 < z < 5.8. The data are compared to two theoretical τ distributions: a model distribution based on the density distribution of Miralda-Escudé et al. (2000) (MHR00), and a lognormal distribution. We assume a...

Degradation experiments are usually used to assess the lifetime distribution of highly reliable products which are not likely to fail under the traditional life tests or accelerated life tests. Several factors, such as the inspection frequency, the sample size and the termination time, are closely related to the experimental cost and the estimation precision. Obviously, an inappropriate setting...

Prevalence and counts of Salmonella Typhimurium in fresh pork sausage packs at the point of retail were modeled by using Irish and United Kingdom retail surveys' data. A methodology for modeling a second-order distribution for the initial Salmonella concentration (lambda0) in pork sausage at retail was presented considering the uncertainty originated from the most probable-number (MPN) serial d...

A type of diagram is proposed as microstructure model of polycrystalline materials, Voronoi diagram in the Laguerre geometry based on random closed packing of spheres (RCP-LV diagram), and discussed in detail. The volumes of spheres are set to serve lognormal distribution, which is strongly inherited by distribution of cell volumes in the RCP-LV diagram. The geometrical and topological properti...

The discovery of two fundamental laws concerning cellular dynamics with recursive growth is reported. Firstly, the chemical abundances measured over many cells were found to obey a log-normal distribution and secondly, the relationship between the average and standard deviation of the abundances was found to be linear. The ubiquity of these laws was explored both theoretically and experimentall...

To be consistent with Extreme Value Theory the pricing of excess-of-loss reinsurance contracts should be based on Pareto type distributions. In this context, two recent Pareto type distributions are considered and compared. The state of a geometric Brownian motion after an exponentially distributed random time with log-normally distributed initial state generates a four-parameter Pareto type di...

Gene trees of holoparasitic plants usually show distinctly longer branch lengths than seen in photosynthetic closest relatives. Such substitution rate jumps have made it difficult to infer the absolute divergence times of parasites. An additional problem is that parasite clades often lack a fossil record. Using nuclear and mitochondrial DNA sequences of Apodanthaceae, a worldwide family of endo...

The formation of stars is inextricably linked to the structure of their parental molecular clouds. Here we take a number of nearby giant molecular clouds (GMCs) and analyse their column density and mass distributions. This investigation is based on four new all-sky median colour excess extinction maps determined from 2MASS. The four maps span a range of spatial resolution of a factor of eight. ...

Generalized linear models might not be appropriate when the probability of extreme events is higher than that implied by the normal distribution. Extending the method for estimating the parameters of a double Pareto lognormal distribution (DPLN) in Reed and Jorgensen (2004), we develop an EM algorithm for the heavy-tailed Double-Pareto-lognormal generalized linear model. The DPLN distribution i...