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

Ayyub Sheikhi; Fereshteh Arad; Radko Mesiar — 2022

Kybernetika

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 $Z \overset{d}{=} (X | Y \in T)$ . 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.

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