Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce the variety of self-affine time series exhibiting power spectral density S(f) scaling as a power of the frequency f . Furthermore, we a...

We study shock statistics in the scalar conservation law ∂tu+∂xf(u) = 0, x ∈ R, t > 0, with a convex flux f and random initial data. We show that a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps) is preserved by the entropy solution to the conservation law and we derive kinetic equations that describe the evolution ...

A life distribution and its survival function F = 1 F with finite mean y = /q F(x)dx are said to be HNBUE (HNWUE) if F(x)dx < (>) U exp(-t/y) for t > 0. The major part of this thesis deals with the class of HNBUE (HNWUE) life distributions. We give different characterizations of the HNBUE (HNWUE) property and present bounds on the moments and on the survival function F when this is HNBUE (HNWUE...

A class of empirical distributions is introduced which are based on various weighted linear combinations of order statistics, and which have convergence properties the classical empirical distribution does not, or which stochastically or convexly dominate the classical empirical distribution. In estimating an unknown probability distribution F based on a sequence of iid observations XI, X2, . ....

This article addresses two important themes in early visual computation: First, it presents a novel theory for learning the universal statistics of natural images—a prior model for typical cluttered scenes of the world—from a set of natural images, and, second, it proposes a general framework of designing reaction-diffusion equations for image processing. We start by studying the statistics of ...

Meta-analysis of genetic data must account for differences among studies including study designs, markers genotyped, and covariates. The effects of genetic variants may differ from population to population, i.e., heterogeneity. Thus, meta-analysis of combining data of multiple studies is difficult. Novel statistical methods for meta-analysis are needed. In this article, functional linear models...

Meta-analysis of genetic data must account for differences among studies including study designs, markers genotyped, and covariates. The effects of genetic variants may differ from population to population, i.e., heterogeneity. Thus, meta-analysis of combining data of multiple studies is difficult. Novel statistical methods for meta-analysis are needed. In this article, functional linear models...

Joseph S. Verducci, Vincent F. Melfi, Shili Lin, Zailong Wang, Sashwati Roy, and Chandan K. Sen Laboratory of Molecular Medicine and DNA Microarray Facility, Davis Heart and Lung Research Institute, Department of Surgery, Department of Statistics, and Mathematical Biosciences Institute, The Ohio State University, Columbus, Ohio; Department of Statistics, Michigan State University, East Lansing,...

Christopher F. H. Nam, John A. D. Aston, Idris A. Eckley, Rebecca Killick Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK Statistical Laboratory, DPMMS, University of Cambridge, Cambridge, CB3 0WB, UK Department of Mathematics and Statistics, University of Lancaster, Lancaster, LA1 4YF, UK {c.f.h.nam | j.a.d.aston }@warwick.ac.uk {i.eckley | r.killick }@lancaster.ac.uk Fe...

Lorraine Shack *, Heather Bryant , Gina Lockwood , Larry F. Ellison d a Population and Public Health, Alberta Health Services, Calgary, Canada Divisions of Oncology and Community Health Sciences, University of Calgary, Calgary, Canada Canadian Partnership Against Cancer, 1 University Ave., Suite 300, Toronto, ON M5J 2P1, Canada Health Statistics Division, Statistics Canada, Ottawa, ON, Canada