A note on GG-normal distributions

As is known, the convolution μ∗νμ∗ν of two GG-normal distributions μ,νμ,ν with different intervals of variances may not be GG-normal. We show that μ∗νμ∗ν is a GG-normal distribution if and only if σ¯μσ¯μ=σ¯νσ¯ν.