For the point and interval estimation of the scale and shape parameters of the Lomax distribution, the frequentist method is invalid and the Bayesian method is sometimes inefficient when the coefficient of variation is less than one. In particular, when the coefficient of variation and the sample size are small, the phenomenon is getting worse that one needs to develop an effective and robust approach. In this paper, the generalized fiducial method is employed to estimate the parameters of interest and compared with the frequentist and Bayesian methods. Simulation results show that the generalized fiducial interval is slightly conservative while often having average length comparable or shorter than Bayesian methods, and the generalized fiducial median estimator often has a much smaller mean square error than other point estimators. Finally, a real data set is used to illustrate the new methodology.

对于 Lomax 分布的尺度和形状参数的点和区间估计，当变异系数小于 1 时，频率论方法无效，贝叶斯方法有时效率低下。特别是当变异系数和样本量都很小时，这种现象越来越严重，需要开发一种有效且稳健的方法。本文采用广义基准方法估计感兴趣的参数，并与频率论和贝叶斯方法进行比较。仿真结果表明，广义基准区间略保守，但其平均长度往往与贝叶斯方法相当或更短，并且广义基准中值估计量的均方误差通常比其他点估计量小得多。最后，