Results 1 to 2 of 2

Math Help - Bayesian - Exponential Family

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    9

    Bayesian - Exponential Family

    Im trying to show that the exponential distribution is a member of the exponential family. I can only find examples of normal, binomial and bernoulli as guidance on the web. I know that exponential is conjugate to gamma. Not really sure of the exact process. Please can someone point me in the right direction? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    You just have to factor it into the following form:

    f(x|\beta) = h(x)c(\beta)e^{\sum_{i = 1} ^ k t_i(x)w_i(\beta)}

    for some functions h, c, t_i, w_i, and positive integer k. They can be constant functions if you want. For the exponential density, I'll get you started by giving you

    f(x|\beta) = \frac{1}{\beta}e^{-x/\beta}I_{(0, \infty)}(x) (just so there's no ambiguity, since some people write it differently)
    h(x) = I_{(0, \infty)}(x)
    c(\beta) = \frac{1}{\beta}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inverse Gaussian Exponential Family
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: March 15th 2012, 02:17 PM
  2. Multiparameter exponential family
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 20th 2010, 08:54 AM
  3. exponential family help
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2010, 01:37 PM
  4. Exponential Family
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 4th 2010, 07:32 PM
  5. Exponential Family & Sufficient Statistic.
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: August 19th 2009, 04:45 PM

Search Tags


/mathhelpforum @mathhelpforum