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Maximum likelihood estimation of the parameters of the generalized extreme-value distribution

广义极值分布参数的极大似然估计

Explicit expressions are provided for the information matrix of the three-parameter generalized extreme-value distribution. A condition for regular estimation is established.

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A Mean Difference Estimator of Standard Deviation in Asymmetrically Censored Normal Samples

非对称删失正态样本中标准差的平均差估计量

Healy's adaptation of Downton's linear estimator of the standard deviation suitable for symmetrically censored normal samples is extended to asymmetric censoring. An approximation for the variance of the estimator for all forms of censoring is given and comparisons are made with the exact variances for small samples.

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A mean difference estimator of standard deviation in asymmetrically censored normal samples

非对称删失正态样本中标准差的均差估计量

Healy's adaptation of Downton's linear estimator of the standard deviation suitable for symmetrically censored normal samples is extended to asymmetric censoring. An approximation for the variance of the estimator for all forms of censoring is given and comparisons are made with the exact variances for small samples.

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Selection of Trimming Proportions for Robust Adaptive Trimmed Means

稳健自适应截尾均值的截尾比例选择

Asymptotic variances of trimmed means for a family of symmetric distributions including the uniform, normal, and double exponential are examined and used to suggest forms of adaptive trimmed means as robust estimators of location. The proportions of trimming in the adaptive estimators are based on simple functions of easily obtained measures of nonnormality.

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Variances and Covariances of Order Statistics from the Gamma Distribution

伽马分布次序统计量的方差与协方差

The expectations, variances and covariances of the order statistics in a sample of size n from a standardized gamma distribution with parameter r are tabulated for r = 2(1)5 and n = 2(1)10.

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Variances and covariances of order statistics from the gamma distribution

伽马分布次序统计量的方差与协方差

The expectations, variances and covariances of the order statistics in a sample of size n from a standardized gamma distribution with parameter r are tabulated for r = 2(1)5 and n = 2(1)10.

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Normalizing transformations of Student's t distribution

Student t分布的正态化变换

The accuracies of several normalizing transformations of a t distribution with v degrees of freedom are examined for large and small values of v. Expansions of the inverse transformations in terms of powers of v-1 are produced and the first few terms compared with Fisher's general expansion. For small values of v the transformations are used to determine approximate percentage points of t which are then compared with the exact percentage points.

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Distribution of the normal scores estimator of the standard deviation of a normal population

正态总体标准差的正态得分估计量之分布

The normal scores estimator of the standard deviation of a normal population is an easily obtained unbiased nearly best linear estimator. Its distribution, although difficult to derive explicitly, is shown to be closely approximated by the distribution of cXv/√v, where Xv has a X distribution with v degrees of freedom and c is a scale factor. Exact or approximate values of the parameters c and v are determined which allow the usual tests of significance for the population…

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Use of a simple range-type estimator of σ in tests of hypotheses

在假设检验中使用简单的极差型标准差估计量

A particularly simple range-type estimator of the standard deviation of a normal population having a convenient form for all sample sizes is considered and further results showing its high efficiency are derived. The distribution of this estimator is shown to be closely approximated by a χdistribution with noninteger degrees of freedom. This approximation allows the usual tests of significance for the population parameters to be carried out using existing tables of…

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Estimation of the Standard Deviation of a Normal Population from Doubly Censored Samples Using Normal Scores

利用正态得分从双侧删失样本估计正态总体标准差

Gupta's (1952) estimator of the standard deviation of a normal population, depending only on the expected values of the normal order statistics, is considered and further results showing its high efficiency relative to the best linear estimator for all forms of censoring are given. Tables which facilitate computation of the estimator, based on a sample of size n, are provided for 2 ≤ n ≤ 50 for complete samples and for 21 ≤ n ≤ 25 for censored samples, thereby extending…

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Estimation of the standard deviation of a normal population from doubly censored samples using normal scores

利用正态分数从双侧删失样本估计正态总体标准差

SUMMARY Gupta's (1952) estimator of the standard deviation of a normal population, depending only on the expected values of the normal order statistics, is considered and further results showing its high efficiency relative to the best linear estimator for all forms of censoring are given. Tables which facilitate computation of the estimator, based on a sample of size n, are provided for 2 < n < 50 for complete samples and for 21 < n < 25 for censored samples, thereby…

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