Product Description

Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution.

The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function.

Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.

Product Details

• Amazon Sales Rank: #2043549 in Books
• Published on: 2007-12-19
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 336 pages

Review
"This book can be recommended to researchers in life sciences for the wealth of information about statistics of extremes and density function estimation.  The application to hormesis is interesting for those concerned with this strange positive effect that low doses of toxic substances can have in living organisms." (Biometrics, March 2009)

"It is ideally suited for statisticians, researchers and Ph.D. students in statistics and probability theory.  There is also much to benefit those working and studying a wide range of disciplines from computer science, telecommunications and performance evaluation, to demography and population analysis." (Mathematical Review, Issue 2009e)

From the Back Cover
Nonparametric Analysis of Univariate Heavy-Tailed Data: Research and Practice by Natalia Markovich â Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Heavy-tailed distributions are typical for phenomena in complex multi-component systems. They possess a number of specific features including the slower than exponential decay to zero of the tail, the violation of Cramerâs condition, a possible non-existence of some moments, and sparse observations in the tail of the distribution. Consequently the analysis of such distributions requires unique statistical methods. Nonparametric Analysis of Univariate Heavy-Tailed Data introduces these statistical techniques. It provides a survey of classical results and explores recent developments in the theory of nonparametric estimation of the heavy-tailed probability density function and its application to classification when objects belong to populations distributed with heavy tails, the tail index, high quantiles, the hazard rate, and the renewal function.

The book: