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二项分布参数 n 的估计AI 解读

Estimating the parameter n of the binomial distribution on the basis of r independent observations has been considered sporadically over the years. Many questions regarding asymptotic and small sample properties of moment, maximum likelihood, and related estimators either have been ignored or have received inadequate treatment. A unified and comprehensive study of these topics is given here. We also consider the problem of zero-truncated observations.

存在缺失数据时二元正态分布的最大似然估计AI 解读

The maximum likelihood estimators (m.l.e.) are obtained for the parameters of a bivariate normal distribution with equal variances when some of the observations are missing on one of the variables. The likelihood equation for estimating $\rho$, the correlation coefficient, may have multiple roots but a result proved here provides a unique root which is the m.l.e. of $\rho$. The problem of estimating the difference $\delta$ of the two means is also considered and it is shown…

从不完整泊松样本估计完整样本量AI 解读

Maximum likelihood estimators and a modified maximum likelihood estimator are developed for estimating the zero class from a truncated Poisson sample when the available sample size itself is a random variable. All the estimators considered here are asymptotically equivalent in the usual sense; hence their asymptotic properties are investigated in some detail theoretically as well as by making use of Monte Carlo experiments. One modified estimator appears to be best with…

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从截断泊松样本估计零频类别AI 解读

A procedure for estimating the zero class from a truncated Poisson sample is developed. Asymptotic normality of the estimator is proved so that a confidence interval for the missing zero class can be obtained. An example is given to illustrate the results obtained.

Pearson卡方检验应划分多少组？AI 解读

The asymptotic non-null distribution is obtained for the modified form of the Pearson chi-square statistic studied by Dahiya and Gurland [3]. By utilizing this result the power is obtained for specific alternative distributions in testing for normality. This enables recommendations to be made as to the number of class intervals to be employed in applying the aforementioned modification of the Pearson chi-square test of normality.

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二元分布的拟合优度检验AI 解读

Summary Tests of fit based on generalized minimum χ2 techniques are developed for bivariate distributions. The asymptotic null distribution of the test statistic is χ2 while the asymptotic non-null distribution turns out to be that of a weighted sum of independent non-central χ2 variates. The special case of testing the fit of a bivariate normal distribution is investigated in detail and the power is obtained for several alternative families of bivariate distributions.

采用随机分组区间的 Pearson 卡方拟合检验AI 解读

A modified form of the Pearson x2 test statistic is considered where estimators based on the ungrouped sample are employed in the test statistic as well as in determining the class interval end points. In the case of continuous distributions with location and scale parameters, it is shown here that the null distribution of such a modified test statistic does not depend on the parameters if these are estimated by sample mean and variance. By utilizing known results concerning…

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