# On point estimators for Gamma and Beta distributions

@inproceedings{Papadatos2022OnPE, title={On point estimators for Gamma and Beta distributions}, author={Nickos Papadatos}, year={2022} }

Let X 1 , . . . , X n be a random sample from the Gamma distribution with density f ( x ) = λ α x α − 1 e − λ x / Γ ( α ), x > 0, where both α > 0 (the shape parameter) and λ > 0 (the reciprocal scale parameter) are unknown. The main result shows that the uniformly minimum variance unbiased estimator (UMVUE) of the shape parameter, α , exists if and only if n > 4; moreover, it has ﬁnite variance if and only if n > 6. More precisely, the form of the UMVUE is given for all parametric functions…

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