### Abstract

Language | English |
---|---|

Pages | 691-702 |

Number of pages | 12 |

Journal | Signal Processing |

Volume | 94 |

DOIs | |

Publication status | Published - Jan 2014 |

### Fingerprint

### Keywords

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

### Cite this

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*Signal Processing*, vol. 94, pp. 691-702. https://doi.org/10.1016/j.sigpro.2013.07.009

**Copulas for statistical signal processing (Part I) : extensions and generalization.** / Zeng, Xuexing; Ren, Jinchang; Wang, Zheng; Marshall, Stephen; Durrani, Tariq.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Copulas for statistical signal processing (Part I)

T2 - Signal Processing

AU - Zeng, Xuexing

AU - Ren, Jinchang

AU - Wang, Zheng

AU - Marshall, Stephen

AU - Durrani, Tariq

PY - 2014/1

Y1 - 2014/1

N2 - 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

AB - 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

KW - copulas

KW - statistical signal processing

KW - parameter estimation

KW - arbitrary marginal distributions

UR - http://www.sciencedirect.com/science/article/pii/S0165168413002880

U2 - 10.1016/j.sigpro.2013.07.009

DO - 10.1016/j.sigpro.2013.07.009

M3 - Article

VL - 94

SP - 691

EP - 702

JO - Signal Processing

JF - Signal Processing

SN - 0165-1684

ER -