I want to check if the PDF belongs to the exponential family:

$$f(x|v) = C \exp-\sum\limits_{i=1}^n(x_{i}-v)^4$$

How can this fit into this formula (to check if the pdf belongs to the exponential family)?

$$f(x|\theta) = h(x)c(\theta) \exp \left(\sum_{i=1}^{k} w_{i}(\theta) t_{i}(x) \right)$$

  • 1
    For clarity, do you "want to check if the following PDF belongs to the exponential family"? – gung Nov 21 '16 at 17:23
  • Please register &/or merge your accounts (you can find information on how to do this in the My Account section of our help center), then you will be able to edit & comment on your own question. – gung Nov 21 '16 at 19:22
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    Are you missing some parentheses in the first density? – dsaxton Nov 21 '16 at 19:35
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    Ignore the sum over i, and try to show it for $p(x) \propto \exp(-(x-v)^4)$ by expanding the quartic function. – passerby51 Nov 21 '16 at 21:23

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