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Bivariate distributions with Pareto conditionals. (English) Zbl 0617.62051

For a fixed \(\alpha >0\), the totality of bivariate densities with all conditionals being of the Pareto (\(\alpha)\) form is identified. The resulting family is of the form \[ f(x,y)\propto [1+\lambda_ 1x+\lambda_ 2y+\phi \lambda_ 1\lambda_ 2xy]^{-(\alpha +1)} \] for suitable choices of \(\lambda_ 1\), \(\lambda_ 2\) and \(\phi\).

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
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References:

[1] Arnold, B. C., Pareto Distributions (1983), International Cooperative Publishing House: International Cooperative Publishing House Fairland, Maryland · Zbl 1169.62307
[2] Castillo, E.; Galambos, J., Bivariate distributions with normal conditionals (1985), to appear · Zbl 0711.62042
[3] Mardia, K. V., Multivariate Pareto distributions, Annals of Mathematical Statistics, 33, 1008-1015 (1962) · Zbl 0109.13303
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