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

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 Cramerâ??s 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:
Presents non-asymptotical methods of heavy-tailed data analysis.
Demonstrates preliminary data analysis and how to detect heavy tails and dependence.
Presents the unique data transformations to estimate heavy-tailed probability density function at infinity better.
Discusses a regularization theory of the solution of inverse ill-posed stochastic operator equations, and its application to the estimation of the probability density function, the hazard rate and the identification of Markov models.
Provides and examines smoothing methods of the nonparametric estimates as the key point for accurate approximation.
Features numerous exercises and examples of real-life applications in teletraffic theory, population analysis and finance.

Nonparametric Analysis of Univariate Heavy-Tailed Data assumes only an introductory knowledge of probability theory, statistical methods and functional analysis. It is ideally suited for statisticians, researchers and PhD students in statistics and probability theory. There is also much to benefit those working and studying in a wide range of disciplines from computer science, telecommunications and performance evaluation, to demography and population analysis.