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Mere skladnosti : delo diplomskega seminarja
ID Pal, Barbara (Author), ID Stopar, Nik (Mentor) More about this mentor... This link opens in a new window

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Abstract
Diplomsko delo se osredotoča na analizo mer skladnosti kot pomembnega orodja za merjenje in razumevanje odvisnosti med slučajnimi spremenljivkami. V delu najprej definiramo kopule, matematične strukture, ki omogočajo opis povezave med slučajnimi spremenljivkami neodvisno od njihovih robnih porazdelitev. Skozi Sklarov izrek pokažemo povezavo med kopulami in komulativnimi porazdelitvenimi funkcijami ter podrobno razložimo funkcijo skladnosti Q. Definiramo različne mere skladnosti: Kendallov tau, Spearmanov rho, Ginijev gama in Blomqvistov beta. Za vsako mero skladnosti predstavimo formule, lastnosti in povezave s prej definiranimi koncepti. Posebej se posvetimo povezavi med Kendallovim tau in Spearmanovim rho ter med Blomqvistovim beta in ostalimi tremi merami skladnosti, ki nam z izračunano eno mero skladnosti podajo meje za vrednosti druge. Dodamo tudi primer šibke mere skladnosti. Sklenemo z obravnavo zgleda, kjer izračunamo vrednosti vseh obravnavanih mer in jih primerjamo na grafu. Končni del je posvečen tudi uporabi mer skladnosti v financah. Delo prinaša poglobljeno razumevanje mer skladnosti, njihove matematične osnove in idejo praktične uporabe v financah.

Language:Slovenian
Keywords:kopula, mere skladnosti, Kendallov tau, Spearmanov rho, Ginijev gama, Blomqvistov beta, Spearmanov fi
Work type:Final seminar paper
Typology:2.11 - Undergraduate Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2023
PID:20.500.12556/RUL-150832 This link opens in a new window
UDC:519.2
COBISS.SI-ID:165839875 This link opens in a new window
Publication date in RUL:24.09.2023
Views:498
Downloads:39
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Secondary language

Language:English
Title:Measures of concordance
Abstract:
The thesis focuses on analyzing copula-based measures of concordance as an important tool for quantifying and understanding relationships between random variables. We commence by defining copulas, mathematical structures that enable the description of the relationship between random variables independently of their marginal distributions. Through Sklar's theorem, we emphasize the link between copulas and cumulative distribution functions and elaborate on the copula-based concordance function Q. We define various measures of concordance, including Kendall's tau, Spearman's rho, Gini's gamma and Blomqvist's beta. For each measure, we present formulas, properties and connections with previously established concepts. Notably, we delve into the relationship between Kendall's tau and Spearman's rho, as well as Blomqvist's beta and the other three measures of concordance, which provide bounds for the values of one another when one measure is computed. We also provide an example of a weak measure of concordance. The thesis concludes by addressing a practical case study, where we compute values for all discussed measures and compare them through graphical representation. The final section explores the application of dependence measures in finance. This work offers an in-depth comprehension of dependence measures, their mathematical foundations and an idea of practical implementation in finance.

Keywords:copula, measures of concordance, Kendall's tau, Spearman's rho, Gini's gamma, Blomqvist's beta, Spearman's footrule

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