A Note On $G$-normal Distributions

As is known, the convolution $μ*ν$ of two $G$-normal distributions $μ, ν$ with different intervals of variances may not be $G$-normal. We shows that $μ*ν$ is a $G$-normal distribution if and only if $\frac{\overlineσ_μ}{\underlineσ_μ}=\frac{\overlineσ_ν}{\underlineσ_ν}$.

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