Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Utilizing a unit Gompertz distorted copula to model dependence in anthropometric data

  • Received : 2023.02.25
  • Accepted : 2023.06.05
  • Published : 2023.09.30
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Abstract

In this research, a conversion function and a distortion associated with the conversion function are defined and used to derive a unit power Gompertz distortion. A new family of copulas is built using the global distorted function. Four base copulas, namely Clayton, Gumbel, Frank, and Gaussian, are distorted into the family. Some properties including tail dependence coefficients and tail order are examined. Kendall's tau formula is derived for new copulas when the base copula is Clayton, Gumbel, or Frank. The maximum pseudo-likelihood estimation method is employed, and a simulation study was performed. The log-likelihood and AIC are reported to compare the performance of the fitted copulas. According to the applied data, the results indicate that new distorted copulas with additional parameters improve the fit.

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Acknowledgement

The author is grateful to the anonymous reviewers whose comments/recommendations assisted improve this manuscript.

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