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Dear colleagues

Good Day;

Let T be a random variable with Gamma distribution:

T~Gamma (n,θ)

What is the probability density function of θ ̂, where

θ ̂= v

_{1}/ v_{2}v

_{1}= a_{0}*T/((n-1) ) + a_{1}*T^{2}/((n-1)(n-2))+ a_{2}*T^{3}/((n-1)(n-2) (n-3))v

_{2}= a_{0}+a_{1}*T/(n-1) + a_{2}*T^{2}/((n-1)(n-2)) , where, a0, a1, a2 are constants.Many thanks in advance

With Best Regards

Huda