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Mere skladnosti: Kendallov tau in Spearmanov ro : delo diplomskega seminarja
ID Špehonja, Marcel (Author), ID Kokol-Bukovšek, Damjana (Mentor) More about this mentor... This link opens in a new window, ID Mojškerc, Blaž (Comentor)

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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.

Language:Slovenian
Keywords:skladnost, kopula, Sklarov izrek, Kendallov tau, Spearmanov ro, skladnostna funkcija
Work type:Bachelor thesis/paper
Organization:FMF - Faculty of Mathematics and Physics
Year:2020
PID:20.500.12556/RUL-120184 This link opens in a new window
UDC:519.2
COBISS.SI-ID:58699779 This link opens in a new window
Publication date in RUL:17.09.2020
Views:885
Downloads:102
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Secondary language

Language:English
Title:Measures of concordance: Kendall's tau and Spearman's rho
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.

Keywords:concordance, copula, Sklar's theorem, Kendall's tau, Spearman's rho, concordance function

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