Kopule za končne porazdelitve

delo diplomskega seminarja

Jaša Štefan (Author), Damjana Kokol-Bukovšek (Mentor), Blaž Mojškerc (Co-mentor)

Abstract

Pri obravnavanju odvisnosti med slučajnimi spremenljivkami pogosto uporabljamo funkcije s posebnimi lastnostmi, ki jim pravimo kopule. Za njih velja, da povezujejo porazdelitvene funkcije posameznih slučajnih spremenljivk z njihovo skupno porazdelitveno funkcijo. Kako so te povezane med sabo, nam pove Sklarov izrek, ki predstavlja teoretično podlago za uporabo kopul v praksi. V statistiki so pripravne, ker lahko s pomočjo kopule porazdelitev slučajnega vektorja ocenimo z ocenjenimi porazdelitvenimi funkcijami slučajnih spremenljivk. Pri ugotavljanju odvisnosti med slučajnimi spremenljivkami si lahko pomagamo tudi z merami odvisnosti. Med njimi sta najpogosteje uporabljeni Kendallov $\tau$ in Spearmanov $\rho$, ki ustrezata Scarsinijevi definiciji in sta posledično meri skladnosti. V primeru zveznih slučajnih spremenljivk je kopula za določeno skupno porazdelitveno funkcijo enolična. V diskretnem primeru pa temu ni več tako. Posledično naletimo na težave, saj se veliko lastnosti ne prenese v diskretni primer. Izkaže se, da teorija kopul v diskretnem primeru ni neuporabna, je pa potrebno biti previden pri njihovi uporabi.

Keywords

finančna matematika;kopule;podkopule;Sklarov izrek;Carleyine meje;skladnost;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL EF - Faculty of Economics
Publisher:	[J. Štefan]
UDC:	519.2
COBISS:	18430041
Views:	853
Downloads:	245
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Copulas on count data
Secondary abstract:	When observing dependence between random variables we often use functions that have special characteristics, called copulas. They link distribution functions of one variable with their joint distribution function. Sklar’s theorem tells us exactly how they are linked together, and this presents theoretical background for using copulas in practice. They are helpful in statistics: we can use them to estimate distribution of random vector by estimating distribution functions of random variables. When measuring dependence between random variables, it can be helpful to use measures of dependence. Two of the most widely used are Kendall’s $\tau$ and Spearman’s $\rho$, and because they meet the criteria of Scarsini’s definition, they are both measures of concordance. In case of continuous random variables, copula linked with joint distribution functions is unique. However in discrete case that is no longer true. Therefore we run into troubles, as a lot of characteristics do not translate from continuous to discrete case. Nevertheless, copula theory can be useful in discrete case as well, but it has to be used with caution.
Secondary keywords:	copula;subcopula;Sklar theorem;Carley bounds;concordance;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	27 str.
ID:	10958875