Displaying similar documents to “Subdiagonal and almost uniform distributions.”

A Characterization of Uniform Distribution

Joanna Chachulska (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous...

Some properties and applications of probability distributions based on MacDonald function

Oldřich Kropáč (1982)

Aplikace matematiky

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In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types x n K n ( x ) , x ≥ 0 , x n K n ( x x ) , x ∈ 𝐑 and x n + 1 K n ( x ) , x ≥ 0 are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and...

On a general structure of the bivariate FGM type distributions

Sayed Mohsen Mirhosseini, Mohammad Amini, Ali Dolati (2015)

Applications of Mathematics

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In this paper, we study a general structure for the so-called Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions. Through examples we show how to use the proposed structure to study dependence properties of the FGM type distributions by a general approach.