基于Logistic总体Ⅱ型截尾样本分布参数的极大似然估计
Maximum Likelihood Estimation Based on Type Ⅱ Censored Sample Parameters of a Logistic Distribution
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摘要: 为研究Logistic分布的拟合优度检验问题等,讨论了基于Logistic分布Ⅱ型截尾样本分布参数的极大似然估计.研究结果表明:在样本大小足够大,样本双侧截尾比为定值条件下,分布参数的极大似然估计存在、惟一、有界,且相合于真实参数;在样本大小足够大,样本双侧截尾比趋于同一定值条件下,分布参数的极大似然估计具有渐近正态性及渐近无偏性.Abstract: In order to study the goodness-of-fit tests of logistic distribution, the author discusses the maximum likelihood estimation based on type Ⅱ censored sample parameters. From this reasearch the following results are obtained: The maximum likelihood estimation of the logistic distribution parameter exists uniquely, has limits and is consistent to the real parameter if the sample size is large enough and its censored ratio of two sides is a constant; The maximum likelihood estimation of the distribution parameter possesses of asymptoptic normality and asymptotic unbias under the same condition.