Can anyone help me prove this, I'm not able to simplify the distribution to find the sufficient statistics, log normalizer, etc.

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    $\begingroup$ Could you write down the pdf in your post? Here is a MathJax tutorial for typesetting math. $\endgroup$ – StubbornAtom May 18 at 11:56
  • $\begingroup$ Apply the algorithm I give at stats.stackexchange.com/a/519715/919. It solves your problem immediately, with little work. $\endgroup$ – whuber May 18 at 14:04

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