Abstract: Under Mlinex loss function, Bayesian estimation and its admissibility for the scale parameter of inverse gamma distribution are discussed for the first time, and the admissibility of the inverse linear form of a sufficient statistics is also analyzed. Then, Monte Carlo simulation is used to clarify the better performance of Bayes estimate than the maximum likelihood and the minimax estimates, which is as good as the uniformly minimum variance unbiased estimate from estimated error for small samples.

Key words: inverse gamma distribution, Mlinex loss function, Bayesian estimation, admissibility