Estimation of the common mean of inverse Gaussian distributions with different scale-like parameters is considered. We study finite sample properties, second-order admissibility and Pitman closeness properties of the Graybill–Deal estimator of the common mean. The best asymptotically normal estimator of the common mean is derived when the coefficients of variations are known. When the scale-like parameters are unknown but ordered, an improved estimator of the common mean is proposed. We also derive estimators of the common mean using the modified profile likelihood method. A simulation study has been performed to compare among the estimators.

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关于估计几个逆高斯分布的共同均值

考虑了具有不同尺度参数的逆高斯分布的共同均值的估计。我们研究了共同均值的 Graybill-Deal 估计量的有限样本属性、二阶可容许性和 Pitman 接近性属性。当变异系数已知时，可以推导出公共均值的最佳渐近正态估计量。当尺度参数未知但有序时，提出了一种改进的共同均值估计器。我们还使用改进的轮廓似然方法推导出共同均值的估计量。已进行模拟研究以在估计器之间进行比较。