Geodesic
On asymmetric distributions of copula related random variables which includes the skew-normal ones
Kybernetika, Tome 58 (2022) no. 6, pp. 984-995.

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Assuming that $C_{X,Y}$ is the copula function of $X$ and $Y$ with marginal distribution functions $F_{X}(x)$ and $F_{Y}(y)$, in this work we study the selection distribution $Z \overset{\mathrm{d}}{=}( X|Y \in T)$. We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.
DOI : 10.14736/kyb-2022-6-0984
Classification : 62Exx, 62H05
Keywords: selection distribution; skew-normal; Gaussian copula 
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Sheikhi, Ayyub; Arad, Fereshteh; Mesiar, Radko. On asymmetric distributions of copula related random variables which includes the skew-normal ones. Kybernetika, Tome 58 (2022) no. 6, pp. 984-995. doi : 10.14736/kyb-2022-6-0984. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2022-6-0984/

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