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Stable Distributions
Ivana Penava (2019)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group
Cite this document

Penava, I. (2019). Stabilne distribucije (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:769257

Penava, Ivana. "Stabilne distribucije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:769257

Penava, Ivana. "Stabilne distribucije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:769257

Penava, I. (2019). 'Stabilne distribucije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 13 November 2019, https://urn.nsk.hr/urn:nbn:hr:126:769257

Penava I. Stabilne distribucije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2019 November 13] Available at: https://urn.nsk.hr/urn:nbn:hr:126:769257

I. Penava, "Stabilne distribucije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:769257

Metadata
TitleStabilne distribucije
Title (english)Stable Distributions
AuthorIvana Penava
MentorDanijel Grahovac (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Probability and Mathematical Statistics Research Group)
Osijek
Defense date and country2019-10-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U radu su iskazane ekvivalentne definicije stabilnih distribucija i pokazani su neki dokazi tih ekvivalencija. Navedeni su najpoznatiji primjeri i iskazana i dokazana najvažnija svojstva stabilnih slučajnih varijabli s naglaskom na specijalne slučajeve normalne, Cauchyjeve, L´evyjeve i Holtsmarkove distribucije. Posebno su obrađene simetrične stabilne slučajne varijable. U nastavku je proširena definicija stabilnih distribucija na multidimenzionalni slučaj. Definirani su stabilni slučajni vektori i njihova karakteristična funkcija. Korištenjem karakteristične funkcije navedena su osnovna svojstva strogo stabilnih slučajnih vektora, simetričnih stabilnih slučajnih vektora te subgaussovskog slučajnog vektora. Napravljena je usporedba sa svojstvima normalnog slučajnog vektora. Na kraju je diskutirana i pokazana na nekoliko primjera primjena stabilnih distribucija.
Abstract (english)
This paper contains equivalent definitions of stable distributions and some proofs of those equivalences. It contains the most known examples as well as presentation and proofs of the most important properties of stable random variables with accent on special cases of Gaussian, Cauchy, L´evy and Holtsmark distribution. Symmetric stable random variables are covered separately. Furthermore, the definition of stable distribution is expanded on a multidimensional case. A stable random vector and its characteristic function are defined. By using the characteristic function, basic properties of strictly stable random vectors, symmetric stable random vectors and subgaussian random vector are expressed. A comparison with the properties of the Gaussian random vector is presented. In the last chapter, the application of stable distributions is discussed and shown on a couple of examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:769257
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2019-10-23 07:50:14