Copulas for statistical signal processing (Part I): extensions and generalization

Xuexing Zeng, Jinchang Ren, Zheng Wang, Stephen Marshall, Tariq Durrani

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Existing works on multivariate distributions mainly focus on limited distribution functions and require that the associated marginal distributions belong to the same family. Although this simplifies problems, it may fail to deal with practical cases when the marginal distributions are arbitrary. To this end, copula function is employed since it provides a flexible way in decoupling the marginal distributions and dependence structure for random variables. Among different copula functions, most researches focus on Gaussian, Student's t and Archimedean copulas for simplicity. In this paper, to extend bivariate copula families, we have constructed new bivariate copulas for exponential, Weibull and Rician distributions. We have proved that the three copula functions of exponential, Rayleigh and Weibull distributions are equivalent, constrained by only one parameter, thus greatly facilitating practical applications of them. We have also proved that the copula function of log-normal distribution is equivalent to the Gaussian copula. Moreover, we have derived the Rician copula with two parameters. In addition, the modified Bessel function or incomplete Gamma function with double integrals in the copula functions are simplified by single integral or infinite series for computational efficiency. Associated copula density functions for exponential, Rayleigh, Weibull, log-normal, Nakagami-m and Rician distributions are also derived
LanguageEnglish
Pages691-702
Number of pages12
JournalSignal Processing
Volume94
DOIs
Publication statusPublished - Jan 2014

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Signal processing
Bessel functions
Weibull distribution
Normal distribution
Computational efficiency
Random variables
Probability density function
Distribution functions
Students

Keywords

  • copulas
  • statistical signal processing
  • parameter estimation
  • arbitrary marginal distributions

Cite this

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title = "Copulas for statistical signal processing (Part I): extensions and generalization",
abstract = "Existing works on multivariate distributions mainly focus on limited distribution functions and require that the associated marginal distributions belong to the same family. Although this simplifies problems, it may fail to deal with practical cases when the marginal distributions are arbitrary. To this end, copula function is employed since it provides a flexible way in decoupling the marginal distributions and dependence structure for random variables. Among different copula functions, most researches focus on Gaussian, Student's t and Archimedean copulas for simplicity. In this paper, to extend bivariate copula families, we have constructed new bivariate copulas for exponential, Weibull and Rician distributions. We have proved that the three copula functions of exponential, Rayleigh and Weibull distributions are equivalent, constrained by only one parameter, thus greatly facilitating practical applications of them. We have also proved that the copula function of log-normal distribution is equivalent to the Gaussian copula. Moreover, we have derived the Rician copula with two parameters. In addition, the modified Bessel function or incomplete Gamma function with double integrals in the copula functions are simplified by single integral or infinite series for computational efficiency. Associated copula density functions for exponential, Rayleigh, Weibull, log-normal, Nakagami-m and Rician distributions are also derived",
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Copulas for statistical signal processing (Part I) : extensions and generalization. / Zeng, Xuexing; Ren, Jinchang; Wang, Zheng; Marshall, Stephen; Durrani, Tariq.

In: Signal Processing, Vol. 94, 01.2014, p. 691-702.

Research output: Contribution to journalArticle

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