Nonparametric Analysis of Univariate Heavy-Tailed Data (eBook)

Research and Practice

Natalia Markovich (Autor)

eBook Download: PDF

2008 | 1. Auflage
336 Seiten
John Wiley & Sons (Verlag)
978-0-470-72359-3 (ISBN)

Infos

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.

Autor

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.

Rezensionen

"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)

Produkt-Details

• Erscheint lt. Verlag: 2.8.2008
• Reihe/Serie: Wiley Series in Probability and Statistics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Control Systems Technology • Datenanalyse • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • Engineering statistics • Regelungstechnik • Statistics • Statistik • Statistik in den Ingenieurwissenschaften
• ISBN-10: 0-470-72359-9 / 0470723599
• ISBN-13: 978-0-470-72359-3 / 9780470723593