A Practical Guide to Heavy Tails

This volume contains a unique collection of mathematical essays that resent a battery of techniques and approaches for the statistical analysis of heavy tailed distributions and processes. The articles cover a number of applications of heavy tailed modeling, running the gamut from insurance and finance, to telecommunications and the World Wide Web, and classical signal/noise detection problems.

Part 1 Applications: heavy tailed probability distributions in the World Wide Web, M.E. Crovella et al; self-similarity and heavy tails - structural modelling of network traffic, W. Willinger et al; heavy tails in high-frequency financial data, U.A. Muller et al; stable paretian modelling in finance - some empirical and theoretical aspects, S. Mittnik et al; risk management and quantile estimation, F. Bassi et al. Part 2 Time series: analyzing stable time series, R.J. Adler et al; inference for linear processes with stable noise, m. Calder, R.A. Davis; on estimating the intensity of long-range dependence in finite and infinite variance time series, M.S. Taqqu, V. Teverovsky; why non-linearities can ruin the heavy tailed modeller's day, S.I. Resnick; periodogram estimates from heavy-tailed data, T. Mikosch; Bayesian inference for time series with infinite variance stable innovations, N. Ravishanker, Z. Qiou. Part 3 Heavy tail estimation: hill, bootstrap and jackknife estimators for heavy tails, O.V. Pictet et al; characteristic function based estimation of stable distribution parameters, S.M. Kogan. D.B. Williams. Part 4 Regression: bootstrapping signs and permutations for regression with heavy tailed errors - a robust resampling, R. LePage et al; linear regression with stable disturbances, J.H. McCulloch. Part 5 Signal processing: deviation from normality in statistical signal processing - parameter estimation with alpha-stable distributions, P. Tsakalides, C.L. Nikias; statistical modelling and receiver design for multi-user communication networks, G.A. Tsihrintzis. Part 6 Model structures: subexponential distributions, C.M. Goldie, C. Kluppelberg; structure of stationary stable processes, J. Rosinski; tail behaviour of some shot noise processes, G. Samorodnitsky. Part 7 Numerical procedures: numerical approximation of the symmetric stable distribution and density, J.H. McCulloch; table of the maximally-skewed stable distributions, J.H. McCulloch, D.B. Panton; multivariate stable distributions - approximation, estimation, simulation and identification, J.P. Nolan; univariate stable distributions -parametrizations and software, J.P. Nolan.