# product of normal and lognormal variates

If x and y are uncorrelated normal variates, x*exp(y) will have a symmetric unimodal distribution with positive excess kurtosis. Has this distribution been named and studied?

• Standard normals $N(0,1)$ or general Normals $N(\mu, \sigma^2)$? And if the latter, do you wish to assume they share the same means and variances or not? May 6 '14 at 13:34
• I think even the simple case of x = N(0,1) and y = N(0,ysd^2) is interesting. Obviously as ysd approaches zero the product x*exp(y) approaches normality, but has the case of ysd >= 1 been studied? May 6 '14 at 13:39