Kybernetika 58 no. 6, 984-995, 2022

On asymmetric distributions of copula related random variables which includes the skew-normal ones

Ayyub Sheikhi, Fereshteh Arad and Radko MesiarDOI: 10.14736/kyb-2022-6-0984


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.


skew-normal, Gaussian copula, selection distribution


62H05, 62Exx


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