Are there any exponential family distributions other than wishart distribution, multivariate normal distribution, Dirichlet distribution, multinomial(or categorical) distribution, Conway-maxwel multinomial distribution?
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3https://en.wikipedia.org/wiki/Exponential_family – user2974951 Mar 31 '22 at 06:48
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When defining an exponential family (Brown, 1987) $$f(x;\theta) = \dfrac{h(x) \exp\{B(\theta)^TR(x)\}}{\int_{\mathfrak X} h(x) \exp\{B(\theta)^TR(x)\}\,\text dx} \qquad x\in\mathfrak X,\theta\in\Theta$$ there is an infinity of choices both for $h(\cdot)$ (which roughly corresponds to the choice of the dominating measure) and for $R(\cdot)$.
Obviously, most of these families of distributions are not associated with a tradename, but they all are different.
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1For an interesting example without a tradename see https://stats.stackexchange.com/questions/432688/exponential-family-definition-appears-vacuous/432766#432766 – kjetil b halvorsen Mar 31 '22 at 13:24