I am looking for a concrete random variable with skew $\gamma_1$ and kurtosis (not excess) $\gamma_2$, where \begin{align} \frac{\gamma_2}{2}-\frac{\gamma_1^2}{3} = 0. \end{align} I alreagy tried mixtures of normal distributions with the density $f(x)= p \varphi(x)+(1-p)\varphi(x-\delta)$ with the standard normal density $\varphi$, but was not able to find a concrete distribution. Does such a random variable exist?
2026-03-25 17:22:28.1774459348
Moments of probability distributions
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