Bias-corrected maximum likelihood estimation of the parameters of the generalized half-normal distribution
Bias-corrected maximum likelihood estimation of the parameters of the generalized half-normal distribution
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DOI：
10.1080/00949655.2017.1413649
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发表时间：
2018-04
影响因子：
1.2
通讯作者：
J. Mazucheli;S. Dey
中科院分区：
文献类型：
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作者：
J. Mazucheli;S. Dey
摘要Cooray和Ananda提出了一种适用于寿命数据建模的双参数广义半正态分布，但其极大似然估计在有限样本下是有偏的。这促使我们为模型的未知参数构造近似无偏估计。本文采用两种方法对广义半正态分布参数的极大似然估计进行了有偏估计。第一种方法是由考克斯和Snell建议的分析方法，第二种方法是基于参数Bootstrap reservation方法。此外，矩量法（MME）用于比较目的。数值证据表明，分析偏差校正估计显着优于他们的Bootstrapped为基础的对应的小样本和中等样本以及MLE和MME。此外，从结果中可以明显看出，形状参数的偏差校正估计比尺度参数的估计性能更好。此外，结果表明，偏差校正方案产生几乎无偏的估计。最后，六个断裂韧性真实的数据集说明我们的方法的应用。
ABSTRACT Cooray and Ananda introduced a two-parameter generalized Half-Normal distribution which is useful for modelling lifetime data, while its maximum likelihood estimators (MLEs) are biased in finite samples. This motivates us to construct nearly unbiased estimators for the unknown parameters of the model. In this paper, we adopt two approaches for bias reduction of the MLEs of the parameters of generalized Half-Normal distribution. The first approach is the analytical methodology suggested by Cox and Snell and the second is based on parametric Bootstrap resampling method. Additionally, the method of moments (MMEs) is used for comparison purposes. The numerical evidence shows that the analytic bias-corrected estimators significantly outperform their bootstrapped-based counterpart for small and moderate samples as well as for MLEs and MMEs. Also, it is apparent from the results that bias- corrected estimates of shape parameter perform better than that of scale parameter. Further, the results show that bias-correction scheme yields nearly unbiased estimates. Finally, six fracture toughness real data sets illustrate the application of our methods.