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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1Could you write down the pdf in your post? [Here](https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference) is a MathJax tutorial for typesetting math. – StubbornAtom May 18 '21 at 11:56
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Apply the algorithm I give at https://stats.stackexchange.com/a/519715/919. It solves your problem immediately, with little work. – whuber May 18 '21 at 14:04