Maximum-Likelihood Estimation of the Parameters of Gamma and Weibull Populations from Complete and from Censored Samples
Maximum-Likelihood Estimation of the Parameters of Gamma and Weibull Populations from Complete and from Censored Samples
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来自完整样本和截尾样本的伽玛和威布尔总体参数的最大似然估计
DOI：
10.1080/00401706.1965.10490304
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发表时间：
1965
期刊：
影响因子：
2.5
通讯作者：
A. H. Moore
中科院分区：
文献类型：
--
作者：
H. Harter;A. H. Moore
给出了从完整样本和删节样本对Gamma和威布尔总体的三个参数进行联合极大似然估计的迭代过程。对于每一个总体，写出了似然函数，并得到了三个最大似然方程。在每种情况下，这三个方程的同时解将产生三个参数的联合最大似然估计。所提出的求解方程的迭代过程适用于三个参数都未知的最一般情况，也适用于其中一个或任何两个参数已知的特殊情况。给出了数值算例，其中n个项目（m≤n）的模拟寿命试验中的前m个失效次数估计参数，使用来自Gamma和Weibull种群的数据，每个种群具有两个不同的形状参数值。
Iterative procedures are given for joint maximum-likelihood estimation, from complete and censored samples, of the three parameters of Gamma and of Weibull populations. For each of these populations, the likelihood function is written down, and the three maximum-likelihood equations are obtained. In each case, simultaneous solution of these three equations would yield joint maximum-likelihood estimators for the three parameters. The iterative procedures proposed to solve the equations are applicable to the most general case, in which all three parameters are unknown, and also to special cases in which any one or any two of the parameters are known. Numerical examples are worked out in which the parameters are estimated from the first m failure times in simulated life tests of n items (m ≤ n), using data drawn from Gamma and Weibull populations, each with two different values of the shape parameter.