For example, does the positive part of the standard normal distribution satisfy sub-gaussian property?

  • 2
    $\begingroup$ $P(\vert X \vert >t)$ is the same for standard normal and one-sided standard normal. $\endgroup$ Commented Jun 12, 2018 at 18:28
  • $\begingroup$ I agree with you. One way of checking the sub-gaussianity by showing the moment generating function of that r.v. is upper bounded by exponential quantity. How do I establish the same for one-sided standard r.v. While doing that, I'm encountering an additional multiplier 2. I'm not sure how to get rid of it. Hope my question is clear. $\endgroup$
    – Ravi Kolla
    Commented Jun 12, 2018 at 19:13
  • $\begingroup$ This question is a simple special case of your subsequent question. $\endgroup$
    – whuber
    Commented Jun 12, 2018 at 19:52
  • $\begingroup$ I don't think that the multiplier matters for sub-gaussianity. But anyway, the multiplier 2 happens in both cases. The normal distribution has two tails (negative - positive) the half normal distribution tail is twice as high, but there is only one tail. $\endgroup$ Commented Jun 13, 2018 at 8:01


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