According to a book, a distribution belongs to the exponential family if it can be written in the form of

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I wrote the Bernoulli distribution as $\exp\Big(y \log\,[{\mu}/{(1-\mu)}] + \log\,(1-\mu)\Big)$. In this case $a(y)=y$, $b(\theta)= \log\,[{\mu}/{(1-\mu)}], c(\theta)=\log(1-\mu)$, but don't know what $d(y)$ is. Any idea what it is and why?

  • $\begingroup$ If you have the entire pdf without using $d$, then won't it be the case that you just have $d(y)=0$? $\endgroup$ – Glen_b Nov 27 '14 at 23:39


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  • $\begingroup$ That is what I thought, but since this is the first case I have come across in which $d(y)=0$, I wasn't sure. $\endgroup$ – Günal Nov 28 '14 at 12:55
  • $\begingroup$ Let me suggest to reread the definition in your book, this seems the simplest way to be sure. $\endgroup$ – Did Nov 28 '14 at 14:15

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