Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions
Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions
复制标题
g-and-k 和广义 g-and-h 分布的数值最大似然估计
DOI：
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发表时间：
2002
影响因子：
2.2
通讯作者：
H. MacGillivray
中科院分区：
文献类型：
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作者：
G. Rayner;H. MacGillivray
计算能力和可用性的不断提高意味着许多以前被认为难以处理或计算难度太大的最大似然估计（MLE）问题现在可以通过数值来解决。然而，ML参数估计的分布，其唯一的解析表达式是作为分位数函数很少受到关注。数值MLE程序的新的家庭的分布，g-和-k和广义g-和-h分布的参数，并在这里进行了研究。包括模拟研究，并使用渐近方法检查的适当性。由于这些分布的一般性，调查不仅是这些分布的数值极大似然估计，但也是初步调查的性能和问题的数值极大似然估计适用于分位数定义的分布一般。数据集也使用这里的程序进行拟合。结果表明，应使用显著大于100的样本量，以通过最大似然法获得可靠的估计。
Continuing increases in computing power and availability mean that many maximum likelihood estimation (MLE) problems previously thought intractable or too computationally difficult can now be tackled numerically. However, ML parameter estimation for distributions whose only analytical expression is as quantile functions has received little attention. Numerical MLE procedures for parameters of new families of distributions, the g-and-k and the generalized g-and-h distributions, are presented and investigated here. Simulation studies are included, and the appropriateness of using asymptotic methods examined. Because of the generality of these distributions, the investigations are not only into numerical MLE for these distributions, but are also an initial investigation into the performance and problems for numerical MLE applied to quantile-defined distributions in general. Datasets are also fitted using the procedures here. Results indicate that sample sizes significantly larger than 100 should be used to obtain reliable estimates through maximum likelihood.