Displaying similar documents to “Operations on distribution functions not derivable from operations on random variables”

On sums of dependent uniformly distributed random variables.

Claudi Alsina, Eduard Bonet (1979)

Stochastica

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We study and solve several functional equations which yield necessary and sufficient conditions for the sum of two uniformly distributed random variables to be uniformly distributed.

Extreme distribution functions of copulas

Manuel Úbeda-Flores (2008)

Kybernetika

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In this paper we study some properties of the distribution function of the random variable C(X,Y) when the copula of the random pair (X,Y) is M (respectively, W) – the copula for which each of X and Y is almost surely an increasing (respectively, decreasing) function of the other –, and C is any copula. We also study the distribution functions of M(X,Y) and W(X,Y) given that the joint distribution function of the random variables X and Y is any copula.

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...