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Displaying similar documents to “The Fréchet transform.”

Dependence Measuring from Conditional Variances

Noppadon Kamnitui, Tippawan Santiwipanont, Songkiat Sumetkijakan (2015)

Dependence Modeling

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A conditional variance is an indicator of the level of independence between two random variables. We exploit this intuitive relationship and define a measure v which is almost a measure of mutual complete dependence. Unsurprisingly, the measure attains its minimum value for many pairs of non-independent ran- dom variables. Adjusting the measure so as to make it invariant under all Borel measurable injective trans- formations, we obtain a copula-based measure of dependence v* satisfying...

Shuffles of Min.

Piotr Mikusinski, Howard Sherwood, Michael D. Taylor (1992)

Stochastica

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Copulas are functions which join the margins to produce a joint distribution function. A special class of copulas called shuffles of Min is shown to be dense in the collection of all copulas. Each shuffle of Min is interpreted probabilistically. Using the above-mentioned results, it is proved that the joint distribution of any two continuously distributed random variables X and Y can be approximated uniformly, arbitrarily closely by the joint distribution of another pair X* and Y* each...