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提高负二项分布与 Neyman A 型分布拟合检验功效的方法AI 解读

A modification of the quadratic form involved in a generalized minimum chi-squared procedure yields the same asymptotic null distribution of the test statistic for testing fit by an assumed model, but a different form of nonnull distribution emerges. This result is applied to testing fit of the negative binomial and Neyman Type A distributions, and tables of asymptotic power are presented that show the increase of power obtained. A numerical example is presented to…

提高负二项分布与Neyman A型分布拟合检验功效的方法AI 解读

A modification of the quadratic form involved in a generalized minimum chi-squared procedure yields the same asymptotic null distribution of the test statistic for testing fit by an assumed model, but a different form of nonnull distribution emerges. This result is applied to testing fit of the negative binomial and Neyman Type A distributions, and tables of asymptotic power are presented that show the increase of power obtained. A numerical example is presented to…

具有超几何概率的一般离散分布族AI 解读

Summary A three-parameter family of distributions which belongs to Kemp's wide class, and which extends a two-parameter family of Katz, is investigated. Relations involving moments and probabilities are utilized in obtaining minimum χ2 estimators of the parameters. The asymptotic relative efficiency of various estimators is compared and a numerical example given.

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.

正态变量二次型的级数展开AI 解读

A differential operator is defined and applied to the gamma density function. By formal mathematical manipulation the resulting function can be identified with linear combinations of independent gamma variates and central and noncentral definite quadratic forms in independent normal variates. Laguerre series expansions in which the choice of parameters is of a general nature are given. These Laguerre series and chi-square, power and Edgeworth series are then compared in the…

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.

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…

复相关系数分布的进一步研究AI 解读

Summary A general class of series expansions for the non-null distribution of the multiple correlation coefficient is presented which contains, as special cases, the three expansions obtained by one of the authors (Gurland, 1968). The rate of convergence is investigated, and the closeness of an approximation to the true distribution is indicated.

负二项分布及其他聚集型分布的拟合检验AI 解读

A test of fit for the negative binomial and other contagious distributions is presented here. The test, is free of certain disadvantages of the Pearson chi-square test ordinarily used. The proposed test statistic, here called XF 2, is constructed from estimators given by Hinz and Gurland [5] which are obtainable through weighted least squares and which were shown to be highly efficient in wide regions of the parameter space. The power of the proposed test procedure is given…

考虑未知方差不等的共同均值无偏估计量组合AI 解读

The problem considered in this paper is how to combine estimators of the common mean from two samples corresponding to normal populations with different unknown variances. Attention is confined to the case where it is known that the variance of one specific population exceeds that of the other. Three classes of unbiased estimators are presented, one of which is based on a preliminary test of significance regarding the ratio of the population variances. The gain achieved by…

负二项及其他聚集型分布的未变换数据分析方法AI 解读

We give a method of analysing data from the Negative Binomial and other generalized Poisson distributions which is free of certain disadvantages that arise when the data are transformed and then subjected to an ordinary analysis of variance. The method of analysis proposed is based on a statistic called XU2 which is constructed from estimators given by Hinz & Gurland (1967 a). This technique can be used for testing a general linear hypothesis relating to untransformed data…

负二项及其他传染型分布原始数据的分析方法AI 解读

We give a method of analysing data from the Negative Binomial and other generalized Poisson distributions which is free of certain disadvantages that arise when the data are transformed and then subjected to an ordinary analysis of variance. The method of analysis proposed is based on a statistic called XU2 which is constructed from estimators given by Hinz & Gurland (1967 a). This technique can be used for testing a general linear hypothesis relating to untransformed data…

方差相等预检验后的均值相等检验AI 解读

In testing equality of means of two Normal populations Student's t -test is not generally applicable when the variances of the two populations may be unequal and their ratio is unknown. In the present paper several procedures are considered whereby a preliminary test is performed to ascertain whether or not the variances may be regarded as equal. On the basis of the outcome of this preliminary test one proceeds to test for equality of means. The optimal choice of the level…

线性函数关系的参数估计AI 解读

SUMMARY A variety of consistent estimators of the parameters of a linear functional relation have been proposed over the years. Some find their basis in least-squares procedures, some in the methods of analysis of variance, some in the method of grouping, and some in diverse other methods. In this paper we generalize a class of estimators suggested originally by the method of grouping, and consider the asymptotic variance of a number of different types of estimators. As a…

方差异质下均值相等检验的小样本表现AI 解读

By using a finite series representation of the distribution of a certain class of statistics, and by utilizing other techniques presented here, two types of statistic are developed for testing the hypothesis of the equality of the means of two normal populations using small sample sizes. One type of statistic, called unilateral, effectively controls the size of the test under variance heterogeneity if it is known a priori that the variance of one specified population is…

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