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Remarks on conditional moments of the free deformed Poisson random variables

Wiktor Ejsmont (2011)

Banach Center Publications

We will show that the conditional first moment of the free deformed Poisson random variables (q = 0) corresponding to operators fulfilling the free relation is a linear function of the regression and the conditional variance also is a linear function of the regression. For this purpose we will first demonstrate some properties of the Wick product and then we will concentrate on the free deformed Poisson random variables.

Remarks on Two Product-like Constructions for Copulas

Fabrizio Durante, Erich Peter Klement, José Quesada-Molina, Peter Sarkoci (2007)

Kybernetika

We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the * -product and the ☆ -product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.

Repeat distributions from unequal crossovers

Michael Baake (2008)

Banach Center Publications

It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibrium distributions of this type. Due to the nonlinear and infinite-dimensional nature of these models, their analysis requires some nontrivial tools from measure theory and functional analysis, which makes them interesting...

Robust estimation of the scale and weighted distributions

Paweł Błażej (2007)

Applicationes Mathematicae

The concept of robustness given by Zieliński (1977) is considered in cases where violations of models are generated by weight functions. Uniformly most bias-robust estimates of the scale parameter, based on order statistics, are obtained for some statistical models. Extensions of results of Zieliński (1983) and Bartoszewicz (1986) are given.

Robust optimality of Gaussian noise stability

Elchanan Mossel, Joe Neeman (2015)

Journal of the European Mathematical Society

We prove that under the Gaussian measure, half-spaces are uniquely the most noise stable sets. We also prove a quantitative version of uniqueness, showing that a set which is almost optimally noise stable must be close to a half-space. This extends a theorem of Borell, who proved the same result but without uniqueness, and it also answers a question of Ledoux, who asked whether it was possible to prove Borell’s theorem using a direct semigroup argument. Our quantitative uniqueness result has various...

Rozdělení t a mnohorozměrná geometrie

Vítězslav Línek (2019)

Pokroky matematiky, fyziky a astronomie

V článku odvozujeme hustotu t rozdělení s využitím n -rozměrné geometrie. Oproti obvyklejším metodám k tomu nepotřebujeme předpoklad normality, postačující je nezávislost mnohorozměrného rozdělení na směru. Kromě základů diferenciálního počtu použijeme k odvození jen vzorec pro povrch n -rozměrné koule. Tento přístup byl inspirován metodami R. A. Fishera.

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