Eliptične porazdelitve in Kendallov tau : delo diplomskega seminarja

Merhar, Urban (author), Bernik, Janez (mentor), Šega, Gregor (comentor)

Diplomsko delo razišče in dokaže povezavo med Pearsonovim korelacijskim koeficientom in Kendallovim tauom za eliptične porazdelitve. Oba korelacijska koeficienta definiramo in med sabo primerjamo. Poleg tega definiramo eliptične porazdelitve in pokažemo, kako jih zapišemo na drugačen način. Z omenjenim zapisom dokažemo, da je vsota dveh eliptičnih porazdelitev z enako nenegativno simetrično matriko prav tako eliptična porazdelitev. Vse skupaj uporabimo, da izpeljemo povezavo med rho in tau za eliptične porazdelitve.

• Language: Slovenian
• Keywords: eliptična porazdelitev, Pearsonov korelacijski koeficient, Kendallov tau
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-131249
• UDC: 519.2
• COBISS.SI-ID: 78718979
• Publication date in RUL: 24.09.2021

Secondary language

• Language: English
• Title: Elliptical distributions and Kendall's tau

Abstract

The thesis investigates and proves the connection between Pearson’s correlation coefficient and Kendall’s tau for elliptical distributions. Both correlation coefficients are defined and compared. In addition, we define elliptical distributions and show how to present them in a different way. This presentation allows us to prove that the sum of two elliptical distributions with the same non-negative symmetric matrix is also an elliptical distribution. As an application the relation between rho and tau for elliptical distributions is derived.

• Keywords: elliptical distribution, Pearson correlation coefficient, Kendall's tau