A conjecture comparing the sum and maximum of i.i.d. half-normal random variables is false, with the disproof method extending to generalized gamma distributions.
On lower limits and equivalences for distribution tails of randomly stopped sums.Bernoulli, 14(2):391–404
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A remark on the comparison of the sum and the maximum of positive random variables
A conjecture comparing the sum and maximum of i.i.d. half-normal random variables is false, with the disproof method extending to generalized gamma distributions.