Density parameter estimation for additive Cauchy-Gaussian mixture

Yuan Chen; Ercan Engin Kuruoglu; Hing Cheung So; Long-Ting Huang; Wen-Qin Wang

doi:10.1109/SSP.2014.6884609

Density parameter estimation for additive Cauchy-Gaussian mixture

Yuan Chen
, Ercan Engin Kuruoglu
, Hing Cheung So
, Long-Ting Huang
, Wen-Qin Wang

Department of Electrical Engineering

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

7 Citations (Scopus)

Abstract

In this paper, a mixture noise model, which is a sum of symmetric Cauchy and zero-mean Gaussian random variables in time domain, is studied. The Cauchy and Gaussian distributions are characterized by the unknown median γ and variance σ², respectively. The probability density function (PDF) and characteristic function (CF) of the mixture are also investigated which are calculated by the convolution of the two PDFs, and product of the two CFs, respectively. Due to the complication of the resultant PDF, typical approaches such as maximum likelihood estimator may not be able to estimate γ and σ² reliably. Based on the resultant CF, we propose to employ the fractional lower-order moment estimator for their computation. Simulation results show the mean square error performance of the proposed method and a comparison with the Cramér-Rao lower bound is also provided. © 2014 IEEE.

Original language	English
Title of host publication	IEEE Workshop on Statistical Signal Processing Proceedings
Publisher	IEEE Computer Society
Pages	197-200
ISBN (Print)	9781479949755
DOIs	https://doi.org/10.1109/SSP.2014.6884609
Publication status	Published - 2014
Event	2014 IEEE Workshop on Statistical Signal Processing, SSP 2014 - Gold Coast, QLD, Australia Duration: 29 Jun 2014 → 2 Jul 2014

Conference

Conference	2014 IEEE Workshop on Statistical Signal Processing, SSP 2014
Place	Australia
City	Gold Coast, QLD
Period	29/06/14 → 2/07/14

Research Keywords

Additive Cauchy-Gaussian
Cauchy distribution
fractional lower-order moment
Gaussian distribution
Voigt function

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10.1109/SSP.2014.6884609

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@inproceedings{d420b4c04ea3401b98450f10a90d9fb6,

title = "Density parameter estimation for additive Cauchy-Gaussian mixture",

abstract = "In this paper, a mixture noise model, which is a sum of symmetric Cauchy and zero-mean Gaussian random variables in time domain, is studied. The Cauchy and Gaussian distributions are characterized by the unknown median γ and variance σ2, respectively. The probability density function (PDF) and characteristic function (CF) of the mixture are also investigated which are calculated by the convolution of the two PDFs, and product of the two CFs, respectively. Due to the complication of the resultant PDF, typical approaches such as maximum likelihood estimator may not be able to estimate γ and σ2 reliably. Based on the resultant CF, we propose to employ the fractional lower-order moment estimator for their computation. Simulation results show the mean square error performance of the proposed method and a comparison with the Cram{\'e}r-Rao lower bound is also provided. {\textcopyright} 2014 IEEE.",

keywords = "Additive Cauchy-Gaussian, Cauchy distribution, fractional lower-order moment, Gaussian distribution, Voigt function",

author = "Yuan Chen and Kuruoglu, \{Ercan Engin\} and So, \{Hing Cheung\} and Long-Ting Huang and Wen-Qin Wang",

year = "2014",

doi = "10.1109/SSP.2014.6884609",

language = "English",

isbn = "9781479949755",

pages = "197--200",

booktitle = "IEEE Workshop on Statistical Signal Processing Proceedings",

publisher = "IEEE Computer Society",

address = "United States",

note = "2014 IEEE Workshop on Statistical Signal Processing, SSP 2014 ; Conference date: 29-06-2014 Through 02-07-2014",

}

Chen, Y, Kuruoglu, EE, So, HC, Huang, L-T & Wang, W-Q 2014, Density parameter estimation for additive Cauchy-Gaussian mixture. in IEEE Workshop on Statistical Signal Processing Proceedings., 6884609, IEEE Computer Society, pp. 197-200, 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014, Gold Coast, QLD, Australia, 29/06/14. https://doi.org/10.1109/SSP.2014.6884609

Density parameter estimation for additive Cauchy-Gaussian mixture. / Chen, Yuan; Kuruoglu, Ercan Engin; So, Hing Cheung et al.
IEEE Workshop on Statistical Signal Processing Proceedings. IEEE Computer Society, 2014. p. 197-200 6884609.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Density parameter estimation for additive Cauchy-Gaussian mixture

AU - Chen, Yuan

AU - Kuruoglu, Ercan Engin

AU - So, Hing Cheung

AU - Huang, Long-Ting

AU - Wang, Wen-Qin

PY - 2014

Y1 - 2014

N2 - In this paper, a mixture noise model, which is a sum of symmetric Cauchy and zero-mean Gaussian random variables in time domain, is studied. The Cauchy and Gaussian distributions are characterized by the unknown median γ and variance σ2, respectively. The probability density function (PDF) and characteristic function (CF) of the mixture are also investigated which are calculated by the convolution of the two PDFs, and product of the two CFs, respectively. Due to the complication of the resultant PDF, typical approaches such as maximum likelihood estimator may not be able to estimate γ and σ2 reliably. Based on the resultant CF, we propose to employ the fractional lower-order moment estimator for their computation. Simulation results show the mean square error performance of the proposed method and a comparison with the Cramér-Rao lower bound is also provided. © 2014 IEEE.

AB - In this paper, a mixture noise model, which is a sum of symmetric Cauchy and zero-mean Gaussian random variables in time domain, is studied. The Cauchy and Gaussian distributions are characterized by the unknown median γ and variance σ2, respectively. The probability density function (PDF) and characteristic function (CF) of the mixture are also investigated which are calculated by the convolution of the two PDFs, and product of the two CFs, respectively. Due to the complication of the resultant PDF, typical approaches such as maximum likelihood estimator may not be able to estimate γ and σ2 reliably. Based on the resultant CF, we propose to employ the fractional lower-order moment estimator for their computation. Simulation results show the mean square error performance of the proposed method and a comparison with the Cramér-Rao lower bound is also provided. © 2014 IEEE.

KW - Additive Cauchy-Gaussian

KW - Cauchy distribution

KW - fractional lower-order moment

KW - Gaussian distribution

KW - Voigt function

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DO - 10.1109/SSP.2014.6884609

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9781479949755

SP - 197

EP - 200

BT - IEEE Workshop on Statistical Signal Processing Proceedings

PB - IEEE Computer Society

T2 - 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014

Y2 - 29 June 2014 through 2 July 2014

ER -

Density parameter estimation for additive Cauchy-Gaussian mixture

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