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This paper introduces a weighted entropic copula from preliminary knowledge of dependence. Considering a copula with common distribution we formulate the weighted entropy dependence model (WMEC). We give an approximator for the copula function of this problem. Also, we discuss some asymptotical properties regarding the unknown parameters of the model.

conditional, This research was partially supported by the KBN 511/2 /91 grant. Key words and phrases: conditional specification, conditional distribution, regression function, conditional Poisson law, bivariate Poisson conditionals distribution. A MS (1980) subject classification: 62H05, 62E10. 238 J. W e s o l o w s k i Ahsanullah and Wesolowski [1] character izat ion of the bivariate normal i ty by the normal conditional distr ibution and the linear m, Wesolowski [1*2] uniqueness theorems for power series conditional distribution and a con- sistent m. In this

function H is best characterized by a unique function -a bivariate copula C, defined everywhere on the unit square 12 by the following relation H(x,y) = C(F(x),G(y)), x)2/GR (see Sklar's Theorem, Sklar (1959)). A bivariate copula is a bivariate cu- mulative distribution function with uniform margins on the unit interval I. 2000 Mathematics Subject Classification: 62E10, 62H05. Key words and phrases: Copulas, positive quadrant dependence, regression, charac- terizing theorems, Lancaster probabilities, diagonal expansion of bivariate density, or- thonormal polynomials