Analiza Benfordovega zakona

magistrsko delo

Špela Povrženič (Author), Roman Drnovšek (Mentor)

Abstract

Benfordov zakon je empirični zakon, ki nam pove, da se nizke vodilne števke v podatkih iz vsakdanjega sveta pojavijo veliko večkrat kot visoke vodilne števk. Ravno zaradi te lastnosti lahko zakon uporabimo tudi kot forenzičen test pri preverjanju podatkovnih prevar. Benfordov zakon lahko brez problema uporabimo tudi v nekem druge številske sistemu, prav tako pa lahko naše podatke brez problema spreminjamo v druge merske enote in se porazdelitev s tem sploh ne bo spremenila, saj za Benfordov zakon velja načelo invariantnosti. Štirje temeljni numerični procesi, ki nas pripeljejo do znanega gibanja vodilnih števk, pa so proces slučajnih linearnih kombinacij, proces združevanja podatkovnih množic, proces naključnega izbora števil in multiplikativni proces. Pred samo analizo podatkov je nujno potrebno, da ima podatkovna množica čim večji razpon in da ohranimo samo tiste vrednosti, ki so primerne za našo analizo. Za testiranje Benfordovega zakona lahko uporabimo test Z, test hi-kvadrat, pregled odstopanj vsote kvadratov, Savillovo regresijsko mero, test ponavljajočih vrednosti in pa metodo odkrivanja razvojnega vzorca števk. Na koncu testiramo Benfordov zakon na resničnih podatkih o bruto investicijah v nova osnovna sredstva po občinah.

Keywords

Benfordov zakon;numerični procesi;vodilne števke;statistični testi;prevare;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[Š. Povrženič]
UDC:	519.21
COBISS:	18665817
Views:	2505
Downloads:	328
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Benford's Law analysis
Secondary abstract:	Benford's Law is an empirical law which shows us that, in real-world data sets, low digits occur as the leading significant digit much more frequently than high digits do. It is because of this characteristic that we can use Benford's Law as a forensic test in data fraud detection. This law can also be used in other numbering systems. The applied data can be converted in different scale without changing the distribution - this is due to the fact that Benford's Law follows the invariance principle. The four foundamental numerical processes that lead to the known leading digit movement are the linear combinations of random variables process, data set aggregation process, random number selection process and the multiplication process. Before analysing, it is crucial to ensure that the data set has the widest range of data possible and that we retain only those values that are suitable for our analysis. The tests for evaluating conformity to Benford's Law include the Z-test, the chi-square test, the sum of squared deviations, Saville's linear regression analysis, the value repetition test and the digital data pattern detection method. In the end, we test the Benford's Law on the real data in Gross Fixed Capital Formation by municipalities.
Secondary keywords:	Benfordʼs law;numerical processes;leading digits;statistical tests;fraud;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 2. stopnja
Pages:	VII, 72 str.
ID:	11186700