Let X1,...,Xn be a random sample from a gamma distribution with shape parameter α and rate...

Let X1,...,Xn be a random sample from a gamma distribution with shape parameter α and rate β (note that this may be a different gamma specification than you are used to). Then

f(x | α, β) = (βα/Γ(α))*x^(α−1) * e^(−βx). where x, α, β > 0

(a) Derive the equations that yield the maximum likelihood estimators of α and β. Can they be solved explicitly? Hint: don’t forget your maximum checks, and it may help to do some internet searching for the “digamma function”, including plotting for possible values...

(b) Find jointly sufficient statistics for α and β.

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orchestra answered 1 year ago

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