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Abstract "A simple procedure generating a multivariate density function that satisfies high asymmetry and polytonal dependency is defined and studied. Traditional approaches to multivariate distributions develop functions that first establish joint density, with dependency inferred, and often poorly understood, as an adjunct at the end. The result is that separate copula designs, such as the Clayton or skew-T, are sought to capture particular dependency structures. The alternative approach presented here generates a joint density function after the dependency is explicitly predefined. This approach, which we have termed the D distribution, has produced a variety of satisfactory results relating to different univariate and multivariate distributions through the choice of an appropriate dependency transfer function. Here we show a new application of the transfer function to construct the flexible and hence highly applicable D distribution and D copula. This concept is connected to copulas, neural networks, skew normal distributions and conditioning on hidden variables."

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