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Distribution-Function-Based Bivariate Quantiles

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  • Chen, L. -A.
  • Welsh, A. H.

Abstract

We introduce bivariate quantiles which are defined through the bivariate distribution function. This approach ensures that, unlike most multivariate medians or the multivariate M-quartiles, the bivariate quantiles satisfy an analogous property to that of the univariate quantiles in that they partition R2 into sets with a specified probability content. The definition of bivariate quantiles leads naturally to the definition of quantities such as the bivariate median, bivariate extremes, the bivariate quantile curve, and the bivariate trimmed mean. We also develop asymptotic representations for the bivariate quantiles.

Suggested Citation

  • Chen, L. -A. & Welsh, A. H., 2002. "Distribution-Function-Based Bivariate Quantiles," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 208-231, October.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:1:p:208-231
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    References listed on IDEAS

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    1. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
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    Cited by:

    1. Gebizlioglu, Omer L. & Yagci, Banu, 2008. "Tolerance intervals for quantiles of bivariate risks and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1022-1027, June.
    2. Nadja Klein & Thomas Kneib, 2020. "Directional bivariate quantiles: a robust approach based on the cumulative distribution function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 225-260, June.
    3. Daniel A. Griffith, 2021. "Articulating Spatial Statistics and Spatial Optimization Relationships: Expanding the Relevance of Statistics," Stats, MDPI, vol. 4(4), pages 1-18, October.
    4. Belzunce, F. & Castano, A. & Olvera-Cervantes, A. & Suarez-Llorens, A., 2007. "Quantile curves and dependence structure for bivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5112-5129, June.

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