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Math Help - Multiparameter exponential family

  1. #1
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    Multiparameter exponential family

    Let X be distributed as N(\mu, \sigma^2) with n=2 and \theta = (\mu, \sigma) \in R \times R^{+}, where mu and sigma are treated as parameters.. How should I show that this belongs to a two parameter exponential family?
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by serious331 View Post
    Let X be distributed as N(\mu, \sigma^2) with n=2 and \theta = (\mu, \sigma) \in R \times R^{+}, where mu and sigma are treated as parameters.. How should I show that this belongs to a two parameter exponential family?

    Hint: f(x; \theta) belongs to a two parameter exponential family if you can express


    f(x; \theta) = a(\theta).g(x). \mbox{exp} ( \sum_{i=1}^{2} {b_{i}}(\theta). {R_{i}(x)} )

    Now try to express the pdf of your normal dist. in the above form
    Last edited by harish21; May 20th 2010 at 08:11 AM.
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