SCALE PARAMETER OF GAMMA DISTRIBUTION AND ITS AUTO-COVARIANCE ESTIMATION

In this paper, we discover that the scale parameter of a gamma distribution is exactly equal to the covariance of the r. v. and its logarithm. We make use of this property to construct an auto-covariance estimator （ACE） of the parameters of gamma distribution. This new estimator is easier to calculate, better than the moment estimator and closer to the MLE. As the MLE’s are mostly biased and the bias cannot be reduced, the ACE’s may improve the position of the MLE’s in respect of unbiasedness when the size of sample is small. Consistency, asymptotic normality of the ACE’s are discussed also.