Trollfaz
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Wikipedia and some of my simpler statistics courses present the gamma distribution with shape ##\alpha## and rate ##\lambda## as
$$P(X=x)=x^{\alpha-1}\lambda^\alpha e^{-\lambda x} \Gamma(\alpha)$$
Where ##\Gamma(\alpha)## is a value in terms of alpha to normalize the PDF from the space of x from 0 to ##\infty## (i.e make it's integral in the space 1).
I have derived that for integral values of ##\alpha##,
$$\Gamma(\alpha)=\frac{1}{(\alpha-1)!}$$
But how about non integral values of alpha? How do I get the ##\Gamma## constant?
https://en.m.wikipedia.org/wiki/Gamma_distribution
$$P(X=x)=x^{\alpha-1}\lambda^\alpha e^{-\lambda x} \Gamma(\alpha)$$
Where ##\Gamma(\alpha)## is a value in terms of alpha to normalize the PDF from the space of x from 0 to ##\infty## (i.e make it's integral in the space 1).
I have derived that for integral values of ##\alpha##,
$$\Gamma(\alpha)=\frac{1}{(\alpha-1)!}$$
But how about non integral values of alpha? How do I get the ##\Gamma## constant?
https://en.m.wikipedia.org/wiki/Gamma_distribution
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