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单侧与双侧删失正态样本参数的迭代极大似然估计：勘误材料AI 解读

In Table 5, on page 211, the tabular value of AV(μ^) for q1 = 0.0 and q2 = 0.9 should read 0.890, not 0.089. On page 207, on line 1, changes1 to r1; on line 2, change μ to μ^ in the expression for σ^⁠; on line 4, change §5 to §4. The following paper, of which we were not aware at the time our paper was published, should be added to the list of references: ISIDA, M. & TAGAMI, S. (1959). The bias and precision in the maximum likelihood estimation of the parameters of normal…

双端删失样本下第一类极值渐近分布参数的最大似然估计AI 解读

Let X be a random variable having the first asymptotic distribution of smallest (largest) values, with location parameter u and scale parameter b, b > 0. The natural logarithm of the likelihood function of a sample of size n from such a distribution, the lowest r1 and the highest r2 sample values having been censored, is written down and its first and second partial derivatives with respect to the parameters are worked out. The likelihood equations, obtained by equating to…

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完整与删失样本下三参数对数正态分布的局部最大似然估计AI 解读

The natural logarithm of the likelihood function is written down for the m − r order statistics remaining after censoring the n − m largest and the r smallest observations of a sample of size n(0 ≤ r < m ≤ n) from a three-parameter lognormal population. Its first partial derivatives with respect to the parameters, when equated to zero, yield the likelihood equations, and the negatives of its second partial derivatives with respect to the parameters are the elements of the…

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单侧与双侧删失样本下正态总体参数的迭代极大似然估计AI 解读

SUMMARY Iterative procedures are given for joint maximum-likelihood estimation based on singly and doubly censored samples from a normal population. The simultaneous equations yielding the maximum-likelihood estimates are obtained. Since their algebraic solution is impossible, iterative procedures are proposed which are applicable in the most general case in which both parameters are unknown and in special cases in which either of the parameters is known. The asymptotic…

最优替代区间估计量的评价准则及其正态分布应用AI 解读

The following criteria for determining best substitute interval estimators of a given class for a population parameter are considered in this paper: (1) minimizing the expected length of the confidence interval (maximizing the effectiveness); (2) minimizing the sum of the mean (absolute) deviations of the upper and lower confidence bounds from the true value (maximizing the effectivity); and (3) minimizing the sum of the mean squared deviations of the upper and lower…

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最佳替代区间估计量的准则：兼论正态分布的应用AI 解读

The following criteria for determining best substitute interval estimators of a given class for a population parameter are considered in this paper: (1) minimizing the expected length of the confidence interval (maximizing the effectiveness); (2) minimizing the sum of the mean (absolute) deviations of the upper and lower confidence bounds from the true value (maximizing the effectivity); and (3) minimizing the sum of the mean squared deviations of the upper and lower…

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两个样本极差之比的分位点及相应检验的功效AI 解读

In testing the hypothesis that the variances of two populations are equal, a test based on the ration F' of the ranges of two samples, one from each population, is simpler than the conventional F test based on the ratio of the sample variances, and it is only alightly less powerful. Table 1 gives percentage points of the ratio of the rangers of two samples from a normal population which are more extensive and more accurate than any previously published. Table 2 compares the…

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