Nonparametric Analysis of Univariate Heavy-Tailed Data: Research and Practice

Natalia Markovich

Mar 2008 · Sold by John Wiley & Sons

About this ebook

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.

About the author

Natalia Markovich – Institute of Control Sciences, Russian Academy of Sciences, Moscow

Having been the Leading Scientist at the Institute of Control Sciences for the last eleven years, Dr Markovich has had much experience in this area. An extremely active member of the statistical community, she has presented many seminars and invited talks, as well as being involved in numerous international research projects. She has published over 50 articles and has written chapters in two books, for Springer-Verlag and Elsevier.