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Does the standard normal distribution have a heavy right tail? How to prove it? Does the standard log-normal distribution have a heavy right tail? How to prove it?

Thanks!

Richard Hardy
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    The best way to talk about heavy tails is to make comparisons between distribution, for example, that the Cauchy distribution has heavier tails than the Normal Distribution. A measure for calculating the heaviness of tails of a distribution is the Kurtosis. So, I would suggest calculating the Kurtosis for the distributions that you asked and compare their values. – Fiodor1234 Jan 03 '21 at 13:38
  • First, you need a definition of "heaviness of tail." There are infinitely many, so you need to pick one before doing the math. – BigBendRegion Jan 03 '21 at 15:07
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    For other threads about tails of lognormal distributions, see https://stats.stackexchange.com/search?q=lognormal+tail. @Fiodor Several people have argued here, rather strongly, that kurtosis is not a measure of the weight of a tail of a distribution. You can find some of those discussions at https://stats.stackexchange.com/search?q=tail+heavy+kurtosis. Glen_b's account at https://stats.stackexchange.com/a/172532/919 is thoughtful. – whuber Jan 03 '21 at 15:49

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