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![]( "Buchcover ISBN 9780470723593")
„This book can be recommended to researchers in life sciences forthe wealth of information about statistics of extremes and densityfunction estimation. The application to hormesis isinteresting for those concerned with this strange positive effectthat 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 alsomuch to benefit those working and studying a wide range ofdisciplines from computer science, telecommunications andperformance evaluation, to demography and population analysis.“(Mathematical Review, Issue 2009e)
Heavy-tailed distributions are typical for phenomena in complexmulti-component systems such as biometry, economics, ecologicalsystems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of suchdistributions requires special methods of estimation due to theirspecific features. These are not only the slow decay to zero of thetail, but also the violation of Cramer's condition, possiblenon-existence of some moments, and sparse observations in the tailof the distribution. The book focuses on the methods of statistical analysis ofheavy-tailed independent identically distributed random variablesby empirical samples of moderate sizes. It provides a detailedsurvey of classical results and recent developments in the theoryof 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 theestimates, and results for the samples of moderate sizes supportedby Monte-Carlo investigation, are considered. The text isillustrated by the application of the considered methodologies toreal data of web traffic measurements.
Both asymptotical results, for example convergence rates of theestimates, and results for the samples of moderate sizes supportedby Monte-Carlo investigation, are considered. The text isillustrated by the application of the considered methodologies toreal data of web traffic measurements.
