Stabilne razdiobe i primjene

master's thesis

• Author: Magdalena Horvat
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Nikola Sandrić (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-11-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog diplomskog rada bio je najprije definirati stabilnu slučajnu varijablu te iznijeti osnovna svojstva stabilnosti na primjerima slučajnih varijabli koje su nam poznate - normalne, Cauchyjeve i Levyjeve. Nakon toga smo uveli karakterizaciju stabilne slučajne varijable koja proizlazi iz generaliziranog centralnog graničnog teorema i karakterizaciju stabilne slučajne varijable pomoću karakteristične funkcije te smo pomoću njih pokazali razna zanimljiva svojstva ovih slučajnih varijabli. Konačno, pokazali smo i na koji način možemo simulirati stabilne slučajne varijable te smo ilustrirali korištenje programa STABLE za procjenu parametara stabilne slučajne varijable na danim podacima.

Abstract (english)

The aim of this diploma thesis is to define a stable random variable and to outline basic stability properties on the known random variables — the normal one, the Cauchy one and the Levy one. After that, we introduced the characterization of a stable random variable, which follows from the generalized central limit theorem and the characterization of a stable random variable in terms of its characteristic function, and consequently we showed various interesting properties of these random variables. Finally, we have demonstrated how we can simulate stable random variables and we have illustrated the use of the STABLE program for estimating parameters of a stable random variable on the given data.

• Keywords: stabilna slučajna varijabla; normalne slučajne varijable; Cauchyjeve slučajne varijable; Levyjeve slučajne varijable; STABLE
• Keywords (english): stable random variable; normal random variable; Cauchy random variable; Levy random variable; STABLE
• Language: croatian
• URN:NBN: urn:nbn:hr:217:724051
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-05-24 10:34:33