Problems with maximum likelihood estimation and the 3 parameter gamma distribution
Problems with maximum likelihood estimation and the 3 parameter gamma distribution
复制标题
DOI：
10.1080/00949650213534
复制
发表时间：
2002-01-01
影响因子：
1.2
通讯作者：
Shenton, LR
中科院分区：
文献类型：
--
作者：
Bowman, KO;Shenton, LR
涉及的三个参数是标度a、形状Rho和位置S。最大似然估计是((A)超过上限，(Rho)超过上限，(S)超过上限)。利用最近关于二阶方差、偏度和峰度的工作，我们证实了这样一个事实：如果要估计位置参数S，则渐近方差仅当Rho>；2时存在，渐近偏度仅当Rho>；3时存在，而二阶方差和三阶四次中心矩仅当Rho>；4时存在。这些限制的结果是，通常可能需要很大的样本容量来避免推理问题。我们还包括了所考虑的极大似然估计的渐近协方差的新的连分式。
The three parameters involved are scale a , shape rho, and location s . Maximum likelihood estimators are ((a) over cap, (rho) over cap, (s) over cap) . Using recent work on the second order variances, skewness, and kurtosis we establish the facts, that if the location parameter s is to be estimated, then the asymptotic variances only exist if rho>2, asymptotic skewness only exists if rho>3, and 2nd order variances and third order fourth central moments only exist if rho>4. The result of these limitations is that in general very large sample sizes may be needed to avoid inference problems. We also include new continued fractions for the asymptotic covariances of the maximum likelihood estimators considered.