Multivariate Asymmetric Distributions of Copula Related Random Variables
It is known that normal distribution plays an important role in analysing symmetric data. However, this symmetric assumption may not hold in many real word and in such cases, asymmetric distribution, including skew normal distribution, are known as the best alternative. Constructing asymmetric d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Austrian Statistical Society
2023-07-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1446 |
| _version_ | 1797749896986492928 |
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| author | Ayyub Sheikhi Freshteh Arad Radko Mesiar |
| author_facet | Ayyub Sheikhi Freshteh Arad Radko Mesiar |
| author_sort | Ayyub Sheikhi |
| collection | DOAJ |
| description |
It is known that normal distribution plays an important role in analysing symmetric data. However, this symmetric assumption may not hold in many real word and in such cases, asymmetric distribution, including skew normal distribution, are known as the best alternative. Constructing asymmetric distributions is carried out using the conditional/selection approach of several independent variable conditioning on other set of variables and this approach does not work well when the independence between variables
violated. In this work we construct an asymmetric distribution when variables are dependent using a copula. Specifically, we consider the random vectors X and Y are connected using a copula function CX,Y and we study the selection distribution Z = (X|Y ∈ T ).
We present some special cases of our proposed distribution, among them, multivariate skew-normal distribution. Some properties such as moments and moment generating function are investigated. Also, numerical analysis including simulation study as well as
a real data set analysis are presented for illustration.
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| first_indexed | 2024-03-12T16:26:11Z |
| format | Article |
| id | doaj.art-2897e2220f7544f88a432a6c7a877fe1 |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-03-12T16:26:11Z |
| publishDate | 2023-07-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-2897e2220f7544f88a432a6c7a877fe12023-08-08T18:04:45ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2023-07-0152410.17713/ajs.v52i4.1446Multivariate Asymmetric Distributions of Copula Related Random VariablesAyyub Sheikhi0Freshteh AradRadko MesiarShahid BAhonar Univ of Kerman It is known that normal distribution plays an important role in analysing symmetric data. However, this symmetric assumption may not hold in many real word and in such cases, asymmetric distribution, including skew normal distribution, are known as the best alternative. Constructing asymmetric distributions is carried out using the conditional/selection approach of several independent variable conditioning on other set of variables and this approach does not work well when the independence between variables violated. In this work we construct an asymmetric distribution when variables are dependent using a copula. Specifically, we consider the random vectors X and Y are connected using a copula function CX,Y and we study the selection distribution Z = (X|Y ∈ T ). We present some special cases of our proposed distribution, among them, multivariate skew-normal distribution. Some properties such as moments and moment generating function are investigated. Also, numerical analysis including simulation study as well as a real data set analysis are presented for illustration. https://www.ajs.or.at/index.php/ajs/article/view/1446 |
| spellingShingle | Ayyub Sheikhi Freshteh Arad Radko Mesiar Multivariate Asymmetric Distributions of Copula Related Random Variables Austrian Journal of Statistics |
| title | Multivariate Asymmetric Distributions of Copula Related Random Variables |
| title_full | Multivariate Asymmetric Distributions of Copula Related Random Variables |
| title_fullStr | Multivariate Asymmetric Distributions of Copula Related Random Variables |
| title_full_unstemmed | Multivariate Asymmetric Distributions of Copula Related Random Variables |
| title_short | Multivariate Asymmetric Distributions of Copula Related Random Variables |
| title_sort | multivariate asymmetric distributions of copula related random variables |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1446 |
| work_keys_str_mv | AT ayyubsheikhi multivariateasymmetricdistributionsofcopularelatedrandomvariables AT freshteharad multivariateasymmetricdistributionsofcopularelatedrandomvariables AT radkomesiar multivariateasymmetricdistributionsofcopularelatedrandomvariables |