prikaz prve stranice dokumenta Pristranost po veličini
  Download
PDF 292.2 KB
master's thesis
Pristranost po veličini
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:108052
Tomorad, Gabrijel
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Tomorad, G. (2020). Pristranost po veličini (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:108052

Tomorad, Gabrijel. "Pristranost po veličini." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:108052

Tomorad, Gabrijel. "Pristranost po veličini." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:108052

Tomorad, G. (2020). 'Pristranost po veličini', Master's thesis, University of Zagreb, Faculty of Science, accessed 27 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:108052

Tomorad G. Pristranost po veličini [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 November 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:108052

G. Tomorad, "Pristranost po veličini", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:108052

Metadata
TitlePristranost po veličini
AuthorGabrijel Tomorad
MentorBojan Basrak (mentor)
Committee memberBojan Basrak (predsjednik povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
Committee memberMiljenko Huzak (član povjerenstva)
Committee memberZoran Vondraček (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-03-02, 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
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:108052
Study programmeTitle: Finance and Business 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 useLicence In copyright icon
Created on2020-10-27 10:49:13