A01=David Harte
advanced probability methods
Author_David Harte
Boundary Effect
cantor
Cantor Measure
Category=PBT
Category=PHDF
Correlation Exponent
Correlation Integral
dimension
Dimension Estimates
earthquake spatial statistics
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
estimation
exponent
Extended Hypotheses
hausdorff
Hausdorff Dimension
Hill Estimates
Interpoint Distances
large deviation theory
Legendre Transform
Lim Inf
Local Behaviour
Long Range Dependence
measure
Mth Order Statistic
multifractal dimension estimation techniques
Multifractal Measure
Multifractal Spectrums
multinomial
Multinomial Measures
nonlinear dynamical systems
Part Iii
powerlaw
Powerlaw Behaviour
Powerlaw Exponent
Random Cascades
Sampling Measures
Self-similar Stochastic Processes
set
Shallow Events
spatial point pattern modeling
spectrum
statistical fractal analysis
Strongly Bounded
Product details
- ISBN 9781584881544
- Dimensions: 156 x 234mm
- Publication Date: 26 Jun 2001
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
Although multifractals are rooted in probability, much of the related literature comes from the physics and mathematics arena. Multifractals: Theory and Applications pulls together ideas from both these areas using a language that makes them accessible and useful to statistical scientists. It provides a framework, in particular, for the evaluation of statistical properties of estimates of the Renyi fractal dimensions.
The first section provides introductory material and different definitions of a multifractal measure. The author then examines some of the various constructions for describing multifractal measures. Building from the theory of large deviations, he focuses on constructions based on lattice coverings, covering by point-centered spheres, and cascades processes. The final section presents estimators of Renyi dimensions of integer order two and greater and discusses their properties. It also explores various applications of dimension estimation and provides a detailed case study of spatial point patterns of earthquake locations.
Estimating fractal dimensions holds particular value in studies of nonlinear dynamical systems, time series, and spatial point patterns. With its careful yet practical blend of multifractals, estimation methods, and case studies, Multifractals: Theory and Applications provides a unique opportunity to explore the estimation methods from a statistical perspective.
Harte, David
