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Bivariate distributions characterized by one family of conditionals and conditional percentile or mode functions

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  • Arnold, Barry C.
  • Castillo, Enrique
  • Sarabia, José María

Abstract

It is well known that full knowledge of all conditional distributions will typically serve to completely characterize a bivariate distribution. Partial knowledge will often suffice. For example, knowledge of the conditional distribution of X given Y and the conditional mean of Y given X is often adequate to determine the joint distribution of X and Y. In this paper, we investigate the extent to which a conditional percentile function or a conditional mode function (of Y given X), together with knowledge of the conditional distribution of X given Y will determine the joint distribution. Finally, using this methodology a new characterization of the classical bivariate normal distribution is given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:7:p:1383-1392
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    References listed on IDEAS

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    1. Jacek Wesolowski, 1995. "Bivariate distributions via a Pareto conditional distribution and a regression function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 177-183, January.
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    Cited by:

    1. 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.

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