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Finding the mle for the gamma distribution

  1. Nov 12, 2012 #1
    So if the parameter [tex]\theta[/tex] is alpha...

    [tex]L(\theta) = \frac{1}{\Gamma(\theta)\beta^{\theta}} x^{\theta-1} e^{-x/\beta}[/tex]

    Now I take the natural log of that...


    [tex]ln(L(\theta)) = ln(\frac{1}{(1-\theta)!}) + ln(\frac{1}{\beta^{\theta}}) + ln(x^{\theta-1}) + ln(e^{-x/\beta})[/tex]

    Now I want to take the derivative of this...but I'm stuck because I don't know what the derivative of [tex]\frac{1}{(1-\theta)!}[/tex] is...how can I find the derivative of a factorial? :confused:
     
  2. jcsd
  3. Nov 13, 2012 #2
    Why did you replace the gamma function with the factorial in the first place? Differentiate the gamma function, problem solved.
     
  4. Nov 13, 2012 #3

    haruspex

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