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利用 Gibbs 抽样获得条件检验及其应用AI 解读

A random sample is drawn from a distribution which admits a minimal sufficient statistic for the parameters. The Gibbs sampler is proposed to generate samples, called conditionally sufficient or co-sufficient samples, from the conditional distribution of the sample given its value of the sufficient statistic. The procedure is illustrated for the gamma distribution. Co-sufficient samples may be used to give exact tests of fit; for the gamma distribution these are compared for…

摘要暂缺

参数经估计时使用 Moran 统计量的拟合优度检验AI 解读

Moran's log spacings statistic for testing goodness of fit is shown to have the same asymptotic distribution when parameters must be estimated from the sample as it does when parameters are known, provided the estimation is done efficiently. For small samples, a chi-squared approximation is given and shown to be accurate when estimation is carried out by minimizing Mdran's statistic itself regarded as a function of the unknown par ameters. A numerical example is given to…

多样本 Anderson–Darling 检验AI 解读

Two k-sample versions of an Anderson–Darling rank statistic are proposed for testing the homogeneity of samples. Their asymptotic null distributions are derived for the continuous as well as the discrete case. In the continuous case the asymptotic distributions coincide with the (k – 1)-fold convolution of the asymptotic distribution for the Anderson–Darling one-sample statistic. The quality of this large sample approximation is investigated for small samples through Monte…

Shapiro–Wilk 正态性检验 W 统计量的渐近分布AI 解读

Twenty years have elapsed since the Shapiro-Wilk statistic $W$ for testing the normality of a sample first appeared. In that time a number of statistics that are close relatives of $W$ have been found to have a common (known) asymptotic distribution. It was assumed, therefore, that $W$ must have that asymptotic distribution. We show this to be the case and examine the norming constants that are used with all the statistics. In addition the consistency of the $W$ test is…

基于标准化间距的拟合优度检验AI 解读

SUMMARY Normalized spacings provide useful tests of fit for many suitably regular continuous distributions; attractive features of the tests are that they can be used with unknown parameters and also with samples which are censored (Type 2) on the left and/or right. A transformation of the spacings leads, under the null hypothesis, to a set of z-values in (0, 1); however, these are not uniformly distributed except for spacings from the exponential or uniform distributions.…

冯·米塞斯分布的拟合检验AI 解读

Critical points for the asymptotic distribution of Watson's U2 statistic are given for testing the hypothesis that a sample comes from the two-parameter von Mises distribution on the circle when one or more of the parameters is unknown. Monte Carlo results show that convergence to the asymptotic distribution is quick. Dependence of the points on the shape parameter is discussed and seen not to cause any problems.

极值与 Weibull 分布拟合检验的 Kolmogorov 统计量AI 解读

Percentage points are given for the Kolmogorov-Smirnov statistics D +, D -, and D and for the Kuiper statistic V for testing fit to the extreme-value distribution with unknown parameters. The statistics may also be used for tests for the Weibull distribution.

摘要暂缺

Goodness-of-fit tests are given for the logistic distribution, based on statistics calculated from the empirical distribution function. Emphasis is on the statistics W2, U2 and A2, for which asyinptotio percentage points are given, for each of the three cases where one or both of the parameters of the distribution must be estimated from the data. Slight modifications of the calculated statistics are given to enable the points to be used with small samples. Monte Carlo…

基于经验分布函数的逻辑斯蒂分布拟合优度检验AI 解读

Goodness-of-fit tests are given for the logistic distribution, based on statistics calculated from the empirical distribution function. Emphasis is on the statistics W2, U2 and A2, for which asyinptotio percentage points are given, for each of the three cases where one or both of the parameters of the distribution must be estimated from the data. Slight modifications of the calculated statistics are given to enable the points to be used with small samples. Monte Carlo…

关于拟合优度检验的半样本方法AI 解读

Summary Two interesting processes, related to the empirical distribution function, have been pointed out by Rao (1972) and by Durbin (1973). The second, in particular, leads to the half-sample method, an elegant and simple technique for dealing with unknown parameters in goodness-of-fit testing, without the necessity of new tables of percentage points for each distribution tested. to those who have spent some effort in producing such tables, it is natural to wonder whether…

极值分布的拟合优度检验AI 解读

In this paper we present goodness of fit tests for the extreme value distribution, based on the empirical distribution function statistics W2, U2and A2. Asymptotic percentage points are given for each of the three statistics, for the three cases where one or both of the parameters of the distribution must be estimated from the data. Slight modifications of the calculated statistics are given to enable the points to be used with small samples.

极值分布的拟合优度检验AI 解读

In this paper we present goodness of fit tests for the extreme value distribution, based on the empirical distribution function statistics W2, U2and A2. Asymptotic percentage points are given for each of the three statistics, for the three cases where one or both of the parameters of the distribution must be estimated from the data. Slight modifications of the calculated statistics are given to enable the points to be used with small samples.

未知参数下拟合优度统计量的渐近结果AI 解读

Percentage points are given for the asymptotic distributions of the goodness-of-fit statistics $W^2, U^2$ and $A^2$, for the cases where the distribution tested is (a) normal, with mean or variance, or both, unknown; (b) exponential, with scale parameter unknown. Some exact means and variances are also given. The distributions can be expressed as a sum of weighted chi-square variables; the weights are calculated, and the higher cumulants can then be found. The first four…

删失数据的修正 Cramér–von Mises 统计量AI 解读

Cramér-von Mises type statistics are modified so that they can be used to test the goodness of fit of a censored sample, when the distribution function is known completely. Asymptotic percentage points are given, small-sample applications are discussed and asymptotic power considered.

Fisher 分布众数向量的一个新检验AI 解读

The likelihood ratio test is given for the modal vector of a Fisher distribution for the case when the concentration parameter is known. The new test is shown to be more powerful than one previously proposed.

次序统计量协方差矩阵的渐近性质AI 解读

The asymptotic eigenvectors and eigenvalues of V, the covariance matrix of order statistics, are examined, and are given for the case where the parent population is normal or uniform. It is shown how these might, be used in developing a model for goodness-of-fit tests. Some approximations are given for certain functions of V and m, the expected value vector for order statistics, which arise in tests for normality.

次序统计量协方差矩阵的渐近性质AI 解读

The asymptotic eigenvectors and eigenvalues of V, the covariance matrix of order statistics, are examined, and are given for the case where the parent population is normal or uniform. It is shown how these might, be used in developing a model for goodness-of-fit tests. Some approximations are given for certain functions of V and m, the expected value vector for order statistics, which arise in tests for normality.

Fisher 分布众数方向向量的新检验AI 解读

The likelihood ratio test is given for the modal vector of a Fisher distribution for the case when the concentration parameter is known. The new test is shown to be more powerful than one previously proposed.

基于经验分布函数的拟合优度统计量及若干比较AI 解读

This article offers a practical guide to goodness-of-fit tests using statistics based on the empirical distribution function (EDF). Five of the leading statistics are examined—those often labelled D, W 2, V, U 2, A 2—and three important situations: where the hypothesized distribution F(x) is completely specified and where F(x) represents the normal or exponential distribution with one or more parameters to be estimated from the data. EDF statistics are easily calculated, and…

针对赤道型与双峰备择的方向随机性检验AI 解读

Tests of randomness of directions in three-dimensional space or equivalently tests of uniform distribution of points on the unit sphere are treated. One test is against alternatives, which concentrate probability density near an equator, and the other is against alternatives which concentrate probability density near opposite poleθ in each case the poles are unspecified. The tests are based on the latent roots of the matrix of sums of squares and cross-products of the…

圆周数据的拟合优度统计量及若干比较AI 解读

This paper gives percentage points for one of two statistics introduced by Ajne, suitable for observations on a circle. The power of Ajne's statistic is compared with those of Watson's and Kuiper's statistics for certain alternatives to the null hypothesis.

圆周数据的拟合优度统计量及若干比较AI 解读

This paper gives percentage points for one of two statistics introduced by Ajne, suitable for observations on a circle. The power of Ajne's statistic is compared with those of Watson's and Kuiper's statistics for certain alternatives to the null hypothesis.