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I am running a Metropolis-Hastings MCMC to find the distribution of a parameter that takes real, positive values. I was considering using the truncated normal distribution, and was wondering if I have to correct for asymmetry, since it is a derivation of the (symmetric) normal distribution and all.

Thank you

user2597079
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    Please provide us *your* definition of "truncated Normal distribution." – whuber Aug 22 '18 at 12:53
  • Please, see the edits. – user2597079 Aug 22 '18 at 13:33
  • Thank you for the link to Wikipedia. Have you taken a look at the example PDFs it graphs prominently on the first page? Almost all are asymmetric. What, then, do you mean by "symmetric" and what procedure are you thinking of where you refer to "correct for asymmetry"? – whuber Aug 22 '18 at 13:34
  • I don't know about inferring asymmetry by a graphical approach. In my case, for example, the distribution is truncated to only positive values. Thus, if I have a large mean with low variance, the distribution would be very close to the normal distribution. But again, it is truncated, and I don't know if this would have any meaningful effect on the symmetry. Even though the truncation is at the tail, in theory, it would go to -Infinity, and some small probabilities are being truncated. – user2597079 Aug 22 '18 at 13:59
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    A symmetric continuous distribution, according to standard meanings of "symmetric," will have a bilaterally symmetric PDF: see https://stats.stackexchange.com/questions/28992. Since the examples on Wikipedia are not bilaterally symmetric, they don't represent symmetric distributions. Because this is plain, I suspect you might be using "symmetric" in a different sense, which is why you ought to consider explaining what you mean. – whuber Aug 22 '18 at 14:09
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    I see. I thought to be that, but I just wanted to make sure. Also, I found this: https://stats.stackexchange.com/a/260234/136882, which also helped me figuring out. Thank you! – user2597079 Aug 22 '18 at 14:17
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    That appears to be a symmetric *proposal,* which indeed has an entirely different meaning! – whuber Aug 22 '18 at 14:20

1 Answers1

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Whether a truncated normal distribution is symmetric will depend on how the truncation was done. If you truncate a normal at values that are equidistant from the mean, then the result will be symmetric. If you truncate it at other values (or only on one side) then it will not.

Peter Flom
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