Kopulas un uz tām bāzēta regresija
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Latvijas Universitāte
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Abstract
Darbā tiek aprakstītas divu atkarīgu nepārtrauktu gadījuma lielumu kopulu saime, to būtība. Tiek studētas kopulu īpašības un izvestas tās sadalījuma funkcijas, blīvumu funkcijas un nosacītās sadalījuma funkcijas, uz kuru pamata tiek analīzēta savstarpēja mainīgo regresija. Kā arī tiek doti visbiežāk lietojamu kopulu regresiju līniju piemēri.
Atslēgvārdi: Kopulas, sadalījuma funkcija, blīvuma funkcija, regresija, divdimensiju normālais sadalījums.
In this work the family of copula functions for dependent continuous random variables and their essence are examined. The properties of copulas are studied, distribution functions, cumulative distribution functions and marginal distribution functions are deduced, based on which the mutual regression of variables is analyzed. Also for most often used copulas examples of lines of regressions are given. Key words: Copulas, probability distribution function, cumulative distribution function, regression, bivariate normal distribution.
In this work the family of copula functions for dependent continuous random variables and their essence are examined. The properties of copulas are studied, distribution functions, cumulative distribution functions and marginal distribution functions are deduced, based on which the mutual regression of variables is analyzed. Also for most often used copulas examples of lines of regressions are given. Key words: Copulas, probability distribution function, cumulative distribution function, regression, bivariate normal distribution.