3
$\begingroup$

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?

$\endgroup$
2
  • $\begingroup$ 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? $\endgroup$
    – wolfies
    May 6 '14 at 13:34
  • $\begingroup$ 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? $\endgroup$
    – Fortranner
    May 6 '14 at 13:39
3
$\begingroup$

Minxian Yang terms the distribution of x*exp(y) the normal log-normal mixture and studies its properties in the working paper "Normal Log-normal Mixture: Leptokurtosis, Skewness and Applications". He allows for x and y to be correlated.

$\endgroup$
1
  • 3
    $\begingroup$ Can you expand on your answer a little. please? Can you say anything about its properties? Could you give a complete reference? Out of curiosity, did you find this after you posted? (It's perfectly valid to post a question you already have an answer to, and to answer your own question, so it doesn't matter either way, but my curiosity is biting me.) $\endgroup$
    – Glen_b
    May 7 '14 at 0:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.