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I've seen the definition for a distribution that has a heavy right tail but I can't seem to prove to myself that a distribution has a heavy right tail or not. How would you prove that for the normal and for the log-normal distribution?

Noam_I
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    Apply the definition: it only requires estimating an integral. For additional ideas, see the analyses at https://stats.stackexchange.com/questions/86429 and https://stats.stackexchange.com/questions/168851. – whuber Jan 13 '21 at 14:26
  • Any chance for guidance on applying the limit on this integral for the definition? – Noam_I Jan 13 '21 at 14:55
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    Apply the definition and use the fact that for any $t\gt 0,$ eventually (for sufficiently large positive $x$) $tx \gt (\log x)^2 + \epsilon x$ for some $\epsilon \gt 0.$ (You can take $\epsilon=t/2$ for instance.) – whuber Jan 13 '21 at 15:17

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