Pristranost po veličini

master's thesis

• Author: Gabrijel Tomorad
• Mentor: Bojan Basrak (mentor)
• Committee member: Bojan Basrak (predsjednik povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Zoran Vondraček (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-03-02, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Pristranost po veličini (eng. size bias) poseban je slučaj pristranosti prilikom kojeg je, tokom uzorkovanja, vjerojatnost biranja nekog objekta proporcionalna njegovoj veličini (npr. duljini, težini). Iako je takvo svojstvo nepoželjno u statističkim procjenama, pokazuje se da ima skrivenu i ponekad neočekivanu ulogu u nekim rezultatima iz vjerojatnosti i statistike, posebno u teoriji slučajnih procesa. U ovom radu definiramo pristranost po veličini i pokazujemo osnovna svojstva po veličini pristranih slučajnih varijabli.Opisujemo po veličini pristrane procese i dajemo poveznicu sa teorijom obnavljanja analizirajući pritom paradoks vremena čekanja. Povezujemo uniformnu integrabilnost i napetost te dajemo uvid u Lévyjevu karakterizaciju i beskonačno djeljive distribucije.

Abstract (english)

Size bias is a special case of bias in which, during sampling, the likelihood of selecting an object is proportional to its size (e.g. length, weight). Although such property is undesirable in statistical procedures, it is shown to have a hidden and sometimes unexpected role in some results in probability and statistics, especially in the theory of random processes. In this paper, we define the size bias and show the basic properties of size biased random variables. We describe the size biased processes and provide a link to the theory of renewal while analyzing the waiting time paradox. We connect uniform integrability and tightness and give insight into Lévy’s characterization and infinitely divisible distributions.

• Keywords: pristranost po veličini; teorija slučajnih procesa; Lévyjeva karakterizacija; beskonačno djeljive distribucije
• Keywords (english): size bias; theory of random processes; Lévy’s characterization; infinitely divisible distributions
• Language: croatian
• URN:NBN: urn:nbn:hr:217:108052
• Study programme: Title: Finance and Business Mathematics; 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: 2020-10-27 10:49:13