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Title: Aggregation functions constructed from copulas and semi-copulas
Other Titles: ฟังก์ชันการรวมกลุ่มที่สร้างจากคอปูลาและเซมิคอปูลา
Authors: Varayut Boonyasri
Authors: Santi Tasena
Attapol Kaewkhao
Parkpoom Phetpradap
Varayut Boonyasri
Keywords: Aggregation;Semi-copula;Copula;Construction;Sklar’s theorem
Issue Date: 3-Jan-2024
Publisher: Chiang Mai : Graduate School, Chiang Mai University
Abstract: In this dissertation, we show that the set of aggregation functions constructed by composing semi-copulas and tuples of non-decreasing univariate functions is dense in the set of all aggregation functions. In particular, this construction method works for all strictly increasing aggregation functions. This method also resembles Sklar’s construction of multivariate distribution functions. In addition, we obtain necessary and sufficient conditions for representing aggregation functions in a form of our method. Furthermore, we show that any smooth semi-copulas can be constructed from copulas. Therefore, we can also use copulas and univariate non-decreasing functions to construct (continuous) aggregation functions. This allows us to reuse abundant copula families to construct new aggregation functions. Moreover, we prove that the set of aggregation functions constructed by this method is dense in the set of continuous aggregation functions.
Appears in Collections:SCIENCE: Theses

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