NDLI: Second-order heavy-tailed distributions and tail analysis

Content Provider	IEEE Xplore Digital Library
Author	Aysal, T.C. Barner, K.E.
Copyright Year	1991
Abstract	This correspondence studies the second-order distributions of heavy-tail distributed random variables (RVs). Two models for the heavy-tailed distributions are considered: power law and epsi-contaminated distributions. Special cases of the models considered include 1) RVs formed by the product of two independent, but not necessarily identically distributed, heavy-tailed RVs X and Y, such that Z=XY, and 2) RVs formed through squaring a heavy-tail distributed RV X, such that W=X². Tail analysis of the RVs, their cross terms, and square values shows the ordering of their tail heaviness. The following results hold strictly for power law distributions and, under mild conditions, for epsi-contaminated distributions: The tail of f _Z(x) is heavier than that of f_X(x), and the tail of f_W(x) is heavier than that of f_Z(x), where f _(.)(x) denotes the probability density distribution of the corresponding random variable. The heaviness of the tails indicates that robust methods of sample combination and output determination should be utilized to avoid undue influence of outliers and degradation in performance. As examples, the denoising and frequency-selective filtering problems under the derived cross and square statistics for hyperbolic-tailed and epsi-contaminated models are considered. Simulation results indicate that the weighted myriad (WMY) filter outperforms the weighted median (WM) filter, and the WM filter outperforms the weighted sum [finite-impulse-response (FIR)] filter. The results may be exploited in higher order applications of heavy-tailed distributions in networking, such as data traffic modeling, and in nonlinear signal and image processing, such as polynomial and Volterra filtering
Sponsorship	IEEE Signal Processing Society
Starting Page	2827
Ending Page	2832
Page Count	6
File Size	299172
File Format	PDF
ISSN	1053587X
Volume Number	54
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Probability distribution Finite impulse response filter Tail Random variables Robustness Degradation Noise reduction Frequency Filtering Higher order statistics tail analysis Cross distribution heavy-tailed distributions square distribution
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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