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购买间隔服从逆高斯分布的购买发生模型AI 解读

This paper deals with a new purchase incidence model where the interpurchase time of an individual household is described by a two-parameter inverse Gaussian distribution, and the population heterogeneity is modeled by the natural conjugate family which has truncated t and modified gamma marginals. The model, more flexible than the exponential and one-parameter gamma models previously used for purchase incidence, is applied to consumer panel data on toothpaste purchases and…

多部件应力—强度模型中的可靠性估计AI 解读

A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distributions are exponential with unknown scale parameters. The asymptotic distribution is obtained by expanding the unbiased estimate about the maximum likelihood value and establishing their…

二元指数分布中的独立性检验AI 解读

The problem of testing independence in the bivariate exponential distribution of Marshall and Olkin is considered here with the assumption of identical marginal distributions. It is shown that in spite of the presence of a nuisance parameter, a uniformly most powerful test exists. The test turns out to be the same as the one proposed by Bernis, et al., on a heuristic basis. In addition to demonstrating the optimality property of the test, an easily computable expression is…

Cronholm–Revusky 秩检验的性质AI 解读

Cronholm and Revusky [4] have proposed a rank test based on independent subexperiments for the comparison of a treatment effect with a control when the treatment is destructive but the control produces at most a transient effect. This article provides a thorough study of its performance under two sampling situations. With the aid of a computer, the exact small sample power of the test is evaluated for some important alternatives. A modification of the test is proposed for…

Cronholm–Revusky 秩检验的性质AI 解读

Cronholm and Revusky [4] have proposed a rank test based on independent subexperiments for the comparison of a treatment effect with a control when the treatment is destructive but the control produces at most a transient effect. This article provides a thorough study of its performance under two sampling situations. With the aid of a computer, the exact small sample power of the test is evaluated for some important alternatives. A modification of the test is proposed for…

若干非参数独立性检验的临界值与经验功效比较AI 解读

A class of nonparametric tests based on the third quadrant layer ranks has recently been studied by Woodworth [12] in connection with the problem of testing for independence in a bivariate distribution. In this article exact one-sided rejection regions are tabulated for the normal score layer rank test which is asymptotically locally most powerful for positive dependence in the bivariate normal distribution. The cut-off points are tabulated for sample sizes n = 4(1)9 and…

若干非参数独立性检验的临界值与经验功效比较AI 解读

A class of nonparametric tests based on the third quadrant layer ranks has recently been studied by Woodworth [12] in connection with the problem of testing for independence in a bivariate distribution. In this article exact one-sided rejection regions are tabulated for the normal score layer rank test which is asymptotically locally most powerful for positive dependence in the bivariate normal distribution. The cut-off points are tabulated for sample sizes n = 4(1)9 and…

Hodges 双变量符号检验与圆周分布均匀性检验AI 解读

Ajne (1968) studied a test N for uniformity of a circular distribution. Although his problem was apparently quite different from testing about location of a bivariate distribution to which Hodges's sign test applies, the two tests are, in fact, identical. The null distribution and tables for the N test developed by Ajne in 1968 are essentially a duplication of those for Hodgea's test given earlier (1955–1962). Also it is shown that the Rayleigh test is locally most powerful…

Bennett 二元符号检验渐近效率的一则札记AI 解读

Summary Asymptotic power properties of Bennett's bivariate sign test are studied by computing its Pitman efficiency relative to Hotelling's T2 test corresponding to the translation family of alternatives. The behaviour of the Pitman efficiency in some important special cases is also discussed.