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A complete characterization of bivariate densities using the conditional percentile function

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  • Indranil Ghosh

    (University of North Carolina at Wilmington)

Abstract

It is well known that joint bivariate densities cannot always be characterized by the corresponding two conditional densities. Hence, additional requirements have to be imposed. In the form of a conjecture, Arnold et al. (J Multivar Anal 99:1383–1392, 2008) suggested using any one of the two conditional densities and replacing the other one by the corresponding conditional percentile function. In this article we establish, in affirmative, this conjecture and provide several illustrative examples.

Suggested Citation

  • Indranil Ghosh, 2018. "A complete characterization of bivariate densities using the conditional percentile function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 485-492, July.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:5:d:10.1007_s00184-018-0652-5
    DOI: 10.1007/s00184-018-0652-5
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    References listed on IDEAS

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    1. Barry Arnold & D. Gokhale, 1998. "Distributions most nearly compatible with given families of conditional distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 377-390, December.
    2. Alexandru V. Asimit & Raluca Vernic & Ricardas Zitikis, 2016. "Background Risk Models and Stepwise Portfolio Construction," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 805-827, September.
    3. Arnold, Barry C. & Gokhale, D. V., 1994. "On uniform marginal representation of contingency tables," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 311-316, November.
    4. S. Satterthwaite & T. Hutchinson, 1978. "A generalisation of Gumbel's bivariate logistic distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 25(1), pages 163-170, December.
    5. Arnold, Barry C. & Castillo, Enrique & Sarabia, José María, 1996. "Specification of distributions by combinations of marginal and conditional distributions," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 153-157, February.
    6. Arnold, Barry C. & Castillo, Enrique & Sarabia, José María, 2008. "Bivariate distributions characterized by one family of conditionals and conditional percentile or mode functions," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1383-1392, August.
    7. Alexandru V. Asimit & Raluca Vernic & Riċardas Zitikis, 2013. "Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model," Risks, MDPI, vol. 1(1), pages 1-20, March.
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