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Generalized exponential family of distributions

  1. Mar 27, 2012 #1
    1. The problem statement, all variables and given/known data

    A discrete random variable Y has probability distribution given by

    f(y;β) = (ky2β(y+k))/((β+3)(y+2k)(y+1)1/2)

    2. Relevant equations

    I know that for a pdf to be from generalised exponential family of distribution it can expressed as

    f(y) = exp{(yθ-bθ)/a∅ +c(y,∅)}

    3. The attempt at a solution

    From exp{log(f(y;β))} i got -----> exp[(y+k)log(βy)-(y+2k)log(β+3)+log ky - (1/2)log(y+1)]

    Is this sufficient or does it require further work?
  2. jcsd
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