Order statistics of 1/fα signals

N. R. Moloney, K. Ozogány, Z. Rácz

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Order statistics of periodic, Gaussian noise with 1/fα power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d k= k-x k+1between the kth and (k+1)st largest values of the signal. The result d k∼k -1, known for independent, identically distributed variables, remains valid for 0≤αk∼k (α -3 )/2, emerge for 1k∼k, is obtained for α>5. The spectra of average ordered values ε' k= 1-x k∼kβ is also examined. The exponent β is derived from the gap scaling as well as by relating ε' k to the density of near-extreme states. Known results for the density of near-extreme states combined with scaling suggest that β(α=2)=1/2, β(4)=3/2, and β(∞)=2 are exact values. We also show that parallels can be drawn between ε' k and the quantum mechanical spectra of a particle in power-law potentials.

Original languageEnglish
Article number061101
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume84
Issue number6
DOIs
Publication statusPublished - Dec 1 2011

Fingerprint

Order Statistics
statistics
Scaling
scaling
Extremes
Gaussian Noise
random noise
Power Spectrum
Identically distributed
power spectra
Power Law
Exponent
exponents
Valid
Simulation
simulation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Order statistics of 1/fα signals. / Moloney, N. R.; Ozogány, K.; Rácz, Z.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 84, No. 6, 061101, 01.12.2011.

Research output: Contribution to journalArticle

@article{663c228fbd784ae3a5aee05bb388d687,
title = "Order statistics of 1/fα signals",
abstract = "Order statistics of periodic, Gaussian noise with 1/fα power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d k= k-x k+1between the kth and (k+1)st largest values of the signal. The result d k∼k -1, known for independent, identically distributed variables, remains valid for 0≤αk∼k (α -3 )/2, emerge for 1k∼k, is obtained for α>5. The spectra of average ordered values ε' k= 1-x k∼kβ is also examined. The exponent β is derived from the gap scaling as well as by relating ε' k to the density of near-extreme states. Known results for the density of near-extreme states combined with scaling suggest that β(α=2)=1/2, β(4)=3/2, and β(∞)=2 are exact values. We also show that parallels can be drawn between ε' k and the quantum mechanical spectra of a particle in power-law potentials.",
author = "Moloney, {N. R.} and K. Ozog{\'a}ny and Z. R{\'a}cz",
year = "2011",
month = "12",
day = "1",
doi = "10.1103/PhysRevE.84.061101",
language = "English",
volume = "84",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "6",

}

TY - JOUR

T1 - Order statistics of 1/fα signals

AU - Moloney, N. R.

AU - Ozogány, K.

AU - Rácz, Z.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Order statistics of periodic, Gaussian noise with 1/fα power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d k= k-x k+1between the kth and (k+1)st largest values of the signal. The result d k∼k -1, known for independent, identically distributed variables, remains valid for 0≤αk∼k (α -3 )/2, emerge for 1k∼k, is obtained for α>5. The spectra of average ordered values ε' k= 1-x k∼kβ is also examined. The exponent β is derived from the gap scaling as well as by relating ε' k to the density of near-extreme states. Known results for the density of near-extreme states combined with scaling suggest that β(α=2)=1/2, β(4)=3/2, and β(∞)=2 are exact values. We also show that parallels can be drawn between ε' k and the quantum mechanical spectra of a particle in power-law potentials.

AB - Order statistics of periodic, Gaussian noise with 1/fα power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d k= k-x k+1between the kth and (k+1)st largest values of the signal. The result d k∼k -1, known for independent, identically distributed variables, remains valid for 0≤αk∼k (α -3 )/2, emerge for 1k∼k, is obtained for α>5. The spectra of average ordered values ε' k= 1-x k∼kβ is also examined. The exponent β is derived from the gap scaling as well as by relating ε' k to the density of near-extreme states. Known results for the density of near-extreme states combined with scaling suggest that β(α=2)=1/2, β(4)=3/2, and β(∞)=2 are exact values. We also show that parallels can be drawn between ε' k and the quantum mechanical spectra of a particle in power-law potentials.

UR - http://www.scopus.com/inward/record.url?scp=84555187583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84555187583&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.84.061101

DO - 10.1103/PhysRevE.84.061101

M3 - Article

C2 - 22304034

AN - SCOPUS:84555187583

VL - 84

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 6

M1 - 061101

ER -