Abstract
In this paper the concept of density weighting function (d.w.f.) [6] is reexamined and a new constructive approach to the generation of dependence between random variables based on this concept is proposed. A number of well known classical distributions (including the generalized Farlie-Gumbel-Morgenstern distribution) are reinterpreted and new reparametrizations are introduced. Limits of dependence explained by d.w.f.s are examined. An elementary Lemma (stated here for the case n = 2) which serves as a key for a number of far reaching generalizations can be formulated as follows:
Let h(x,y) be a p.d.f. on the square [0, l]2, symmetric about the line y = x. If the isoprobability contours of h are of the form x-y = k(k ∈ [-1, 1]), and h(x, y) is a strictly monotone function of ∣x-y∣, then marginal densities cannot be uniform.
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Kotz, S., Seeger, J.P. (1991). A New Approach to Dependence in Multivariate Distributions. In: Dall’Aglio, G., Kotz, S., Salinetti, G. (eds) Advances in Probability Distributions with Given Marginals. Mathematics and Its Applications, vol 67. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3466-8_6
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DOI: https://doi.org/10.1007/978-94-011-3466-8_6
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