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正态混合分布抽样下的单样本 t 检验AI 解读

For the one-sample $t$-test a new form of the exact distribution of the test statistic $t^2$ is obtained when sampling from a distribution which is a mixture of two normal distributions. A numerical example is provided to show that the size of the test can differ greatly when sampling from distributions having the same skewness and kurtosis. Contours of equal size are plotted for a particular case in a certain cross section of the parameter space.

总体峰度变化下位置估计量的稳健性AI 解读

We investigate the robustness of various estimators of the mean for two families of symmetric distributions (exponential power and t) indexed by the kurtosis γ and Hogg's (1972) measure of tail thickness Q. For fixed γ or Q, the optimal estimator for one family is often inefficient for the other family. Furthermore, over various ranges of γ or Q some common estimators (e.g., the median) are efficient only for one family. However, other estimators (e.g., some trimmed means…

完整样本或尾部删失样本下 Logistic 分布参数的线性估计AI 解读

In this paper we present the asymptotically best linear unbiased estimators for the location and scale parameters of the logistic distribution based on samples where there may be Type 2 censoring in the tails. Given the amount of censoring, the weights of the estimators can be expressed in simple closed forms. Comparisons of these with the best linear unbiased estimators and the Cramer-Rao lower bounds demonstrate that they have good efficiency even for small samples.

完整或尾部删失样本下 Logistic 分布参数的线性估计AI 解读

In this paper we present the asymptotically best linear unbiased estimators for the location and scale parameters of the logistic distribution based on samples where there may be Type 2 censoring in the tails. Given the amount of censoring, the weights of the estimators can be expressed in simple closed forms. Comparisons of these with the best linear unbiased estimators and the Cramer-Rao lower bounds demonstrate that they have good efficiency even for small samples.

方差不等的两个正态总体均值相等检验的水平与功效AI 解读

A method is developed for obtaining the size and power of a wide class of tests which includes solutions to the Behrens-Fisher problem proposed by various authors. A new test in this class is also developed which controls the size effectively and has high power. A comparison is made with other known tests as regards control of size. The power of the proposed test as well as that of Welch-Aspin is also obtained.