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master's thesis
Benfordova razdioba u analizi valutnog rizika
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. urn:nbn:hr:126:170739
Stanić, Dajana
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Stanić, D. (2017). Benfordova razdioba u analizi valutnog rizika (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:170739

Stanić, Dajana. "Benfordova razdioba u analizi valutnog rizika." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:170739

Stanić, Dajana. "Benfordova razdioba u analizi valutnog rizika." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:170739

Stanić, D. (2017). 'Benfordova razdioba u analizi valutnog rizika', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:170739

Stanić D. Benfordova razdioba u analizi valutnog rizika [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:170739

D. Stanić, "Benfordova razdioba u analizi valutnog rizika", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:170739

Metadata
TitleBenfordova razdioba u analizi valutnog rizika
Title (english)Benford Distribution in Currency Risk Analysis
AuthorDajana Stanić
MentorIvica Martinjak (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberIvica Martinjak (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2017-04-07, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Benfordov zakon, poznat i pod nazivom fenomen prve znamenke, govori o vjerojatnosti pojavljivanja jednoznamenkastog prirodnog broja na pojedinoj poziciji broja. Fenomen prve znamenke je prvi otkrio S. Newcomb u 19. stoljeću. Newcombovo nezapaženo otkriće je popularizirao F. A. Benford, po kojem je zakon dobio naziv. U radu najprije definiramo Benfordov niz i uniformno distribuiran modulo 1 niz. Prikazujemo svojstva takvih nizova i navodimo primjere. Dokazujemo važan teorem za uniformno distribuirane nizove, poznat kao Weylov kriterij. Analogno pojmu Benfordovog niza, razmatramo Benfordovu distribuciju za empirijske podatke i testiramo je na jednostavnom primjeru. Objašnjavamo Zipfov zakon te njegovu povezanost s Benfordovim zakonom. U nastavku uvodimo osnovne pojmove vezane za trgovanje valutama i valutni rizik. Posebni je zadatak ovog rada ispitati prate li valutni tečajevi Benfordovu distribuciju. U tu svrhu analiziramo povijesne podatke za pet valuta. Rezultati dobiveni statističkim testom ukazuju da kretanja valutnih tečajeva slijede Benfordovu razdiobu.
Abstract (english)
Benford’s law, known also as the the first digit phenomenon, is a statement about probability of appearance of single-digit integer in certain number position. The phenomenon of the first digit was first discovered by S. Newcomb in 19th century. It is named after F. A. Benford who rediscovered and popularized Newcomb’s unnoticed discovery. In this thesis we first define Benford sequence and uniformly distributed sequence modulo 1. We show the properties of such sequences and present examples. We prove an important theorem for uniformly distributed sequences, known as Weyl’s criterion. By analogy to the concept of Benford sequence, we study Benford distribution for empirical data and test it on a simple example. We explain Zipf’s law and its relationship with Benford’s law. Furthermore, we introduce the basic concepts related to currency trading and currency risk. In particular, we examine whether exchange rates follow Benford distribution. For this purpose, we analyze historical data for the five currencies. The results obtained with statistical test indicate that exchange rates follow Benford distribution.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:170739
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 useLicence In copyright icon
Created on2017-04-26 10:42:32