论文标题
拟合Lomax分布：最小距离估计器与其他估计技术之间的比较
On fitting the Lomax distribution: a comparison between minimum distance estimators and other estimation techniques
论文作者
论文摘要
在本文中，我们研究了Lomax分布的规模和形状参数的各种估计技术的性能。这些方法包括传统方法，例如最大似然估计器和矩估计器的方法。还包括针对偏差调整的最大似然估计器的版本。此外，包括$ l $ - 大型估计器和概率加权矩估计器等替代基于力矩的估计技术以及三种不同的最小距离估计器。通过广泛的蒙特卡洛研究比较了这些估计量中每一个的有限样本性能。我们发现，没有一个估计器的表现均匀地超过了竞争对手。我们建议使用较小样品使用的最小距离估计器之一，而偏差的最大可能性估计的偏差版本则用于较大的样品。此外，传统最大似然估计器的理想渐近特性使它们吸引了更大的样品。我们还包括一个实际应用，证明了在观察到的数据上使用这些技术。
In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the method of moments estimator. A version of the maximum likelihood estimator adjusted for bias is also included. Furthermore, alternative moment-based estimation techniques such as the $L$-moment estimator and the probability weighted moments estimator are included along with three different minimum distance estimators. The finite sample performances of each of these estimators is compared via an extensive Monte Carlo study. We find that no single estimator outperforms its competitors uniformly. We recommend one of the minimum distance estimators for use with smaller samples, while a bias reduced version of maximum likelihood estimation is recommended for use with larger samples. In addition, the desirable asymptotic properties of traditional maximum likelihood estimators make them appealing for larger samples. We also include a practical application demonstrating the use of the techniques on observed data.
