A Note On $G$-normal Distributions

Yongsheng Song

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arXiv · 1410.8225

A Note On $G$-normal Distributions

Yongsheng Song

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Abstract

As is known, the convolution $\mu*\nu$ of two $G$-normal distributions $\mu, \nu$ with different intervals of variances may not be $G$-normal. We shows that $\mu*\nu$ is a $G$-normal distribution if and only if $\frac{\overline{\sigma}_\mu}{\underline{\sigma}_\mu}=\frac{\overline{\sigma}_\nu}{\underline{\sigma}_\nu}$.

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Yongsheng Song. 2014-10-30. A Note On $G$-normal Distributions. https://arxiv.org/abs/1410.8225

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