On background driving distribution functions (BDDF) for some selfdecomposable variables

Jurek, Zbigniew J.

doi:10.14708/ma.v49i2.7103

Artykuł - szczegóły

Tytuł artykułu

On background driving distribution functions (BDDF) for some selfdecomposable variables

Autorzy

Jurek Zbigniew J.

Treść / Zawartość

Pełne teksty: $C:\Users\k.pilitowska\Desktop\MatAppl_2021_2.pdf [zdalny]$

Identyfikatory

DOI

10.14708/ma.v49i2.7103

Warianty tytułu

Przykłady rozkładów kierujących dla niektórych samorozkładalnych rodzin zmiennych losowych

Języki publikacji

Abstrakty

Many classical variables (statistics) are selfdecomposable. They admit the random integral representations via Levy processes. In this note are given formulas for their background driving distribution functions (BDDF). This may be used for a simulation of those variables. Among the examples discussed are: gamma variables, hyperbolic characteristic functions, Student t-distributions, stochastic area under planar Brownian motions, inverse Gaussian variable, logistic distributions, non-central chi-square, Bessel densities and Fisher z-distributions. Found representations might be of use in statistical applications.

Wiele klasycznych modeli probabilistycznych opiera sie o zmienne losowe samorozkładalne. Maja one losowe reprezentacje całkowe oparte o procesy Lévy’ego. W tej notatce podano wzory dla ich kierujących (generujących) dystrybuant. Takich reprezentacji można używać do symulacji tych zmiennych. Wśród omawianych przykładów są: rozkłady t-Studenta, pole stochastyczne pod planarnymi ruchami Browna, odwrotny rozkład Gaussa, rozkłady logistyczne, niecentralny rozkład chi-kwadrat, rozkład Bessela i rozkłady statystyk Z-Fishera. Podane reprezentację mogą być przydatne w statystyce.

Słowa kluczowe

selfdecomposability gamma distribution chi-square distribution hyperbolic distribution t-Student distribution logistic distribution non-central chi-square distribution Wiener process

samorozkładalność proces Lévy’ego funkcja charakterystyczna rozkłady hiperboliczne rozkład gamma rozkład t-Studenta pole losowe proces Wienera funkcje Bessela rozkład Fishera

Wydawca

Polskie Towarzystwo Matematyczne

Czasopismo

Mathematica Applicanda

Rocznik

2021

Tom

Vol. 49, no. 2

Strony

85--109

Opis fizyczny

Bibliogr. 33 poz., tab.

Twórcy

autor

Jurek Zbigniew J.

zjjurek@math.uni.wroc.pl

University of Wrocław, Institute of Mathematics

https://orcid.org/0000-0002-8557-2854

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).

Typ dokumentu

Bibliografia

Identyfikator YADDA

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