Mere skladnosti

Kendallov tau in Spearmanov ro

Marcel Špehonja (Author), Damjana Kokol-Bukovšek (Mentor), Blaž Mojškerc (Co-mentor)

Abstract

V delu diplomskega seminarja predstavimo najpomembnejši meri skladnosti, Kendallov tau in Spearmanov ro. To sta meri, ki opisujeta odvisnost slučajnih spremenljivk, imenovano skladnost. Sprva bomo definirali meri v primeru slučajnega vzorca, bolj podrobno pa si bomo pogledali skladnost zveznih slučajnih spremenljivk. Za natančnejšo obravnavo Kendallovega tau in Spearmanovega ro potrebujemo funkcijo, imenovano kopula, ki povezuje skupne porazdelitvene funkcije slučajnih vektorjev z njihovimi robnimi porazdelitvami. Teorija kopul je nepogrešljiva pri obravnavi mer skladnosti, zato bomo predstavili najpomembnejše kopule ter jih grafično prikazali. S Sklarovim izrekom bomo postavili temelje za razumevanje in obravnavo skladnostnih mer. Delo bomo zaključili s primerjavo mer Kendallovega tau in Spearmanovega ro ter s prikazom nekaterih najpomembnejših neenakosti med njima.

Keywords

finančna matematika;skladnost;kopule;Sklarov izrek;Kendallov tau;Spearmanov ro;skladnostna funkcija;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.11 - Undergraduate Thesis
Organization:	UL EF - Faculty of Economics
Publisher:	[M. Špehonja]
UDC:	519.2
COBISS:	58699779
Views:	903
Downloads:	102
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Measures of concordance: Kendall's tau and Spearman's rho
Secondary abstract:	In this work, we present the most important measures of concordance, Kendall's tau and Spearman's rho. These measures describe a special dependence of random variables called concordance. First we define both measures in the case of a random sample but we will mostly focus on concordance of continuous random variables. For a more precise study of both measures Kendall's tau and Spearman's rho, we introduce function called copula, which links multivariate joint distribution functions of random vectors with their univariate marginal distributions. It has an indispensable role in a study of measures of concordance. We will prove Sklar's theorem, which will serve as a foundation for understanding measures of concordance. Finally, we will take a look into the relationship between Kendall's tau and Spearman's rho and show the most important inequalities relating both measures.
Secondary keywords:	concordance;copula;Sklar theorem;Kendall tau;Spearman rho;concordance function;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	25 str.
ID:	12039034