๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

High quantile estimation for heavy-tailed distributions

โœ Scribed by N.M. Markovich

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
245 KB
Volume
62
Category
Article
ISSN
0166-5316

No coin nor oath required. For personal study only.

โœฆ Synopsis

Different estimators of high quantiles, such as x c p proposed in [N.M. Markovitch, U.R. Krieger, The estimation of heavy-tailed probability density functions, their mixtures and quantiles. Computer Networks 40 (3) (2002) 459-474], Weissman's estimator x w p and the POT-method are considered. Regarding the estimators x c p and x w p the asymptotic normality of the logarithms of ratios of these estimators to the true value of the quantile is proved. These estimators are applied to real data of Web sessions and pages. Furthermore, bootstrap confidence intervals of x c p and x w p are constructed for modelled data of different heavy-tailed distributions as well as for Web-traffic data.

๐Ÿ“œ SIMILAR VOLUMES

Inference for heavy tailed distributions
Inference for heavy tailed distributions
โœ K.B. Athreya; S.N. Lahiri; Wei Wu ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 585 KB

Let X ~, X 2 .... be a sequence of independent and identically distributed random variables in the domain of attraction of a stable law of order ~ and asymmetry parameter ft. This paper develops some large sample inference procedures for the population mean l/ and parameters ~ and ft. Three differen

Estimation problems for distributions wi
Estimation problems for distributions with heavy tails
โœ Zhaozhi Fan ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 320 KB

We establish estimators for the tail index of heavy-tailed distributions. A large deviation principle is proved. An estimator with U-statistic structure is constructed and its asymptotic normality is established. An estimator based on re-sampling procedure is developed and this provides a possibilit

Moment Estimator for Random Vectors with
Moment Estimator for Random Vectors with Heavy Tails
โœ Mark M. Meerschaert; Hans-Peter Scheffler ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 147 KB

If a set of independent, identically distributed random vectors has heavy tails, so that the covariance matrix does not exist, there is no reason to expect that the sample covariance matrix conveys useful information. On the contrary, this paper shows that the eigenvalues and eigenvectors of the sam