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Statistics: An All-Encompassing Discipline

统计学:一门包罗万象的学科

Although Bayesian nonparametric mixture models for continuous data are well developed, there is a limited literature on related approaches for count data.A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions having variance less than the mean.Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow…

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An approximate likelihood ratio test for a normal mean vector with nonnegative components with application to clinical trials

非负分量正态均值向量的近似似然比检验及临床试验应用

A new multivariate statistic, designed to be sensitive to the alternative hypothesis that a mean vector lies in the positive orthant, rather than to all alternatives or to alternatives on a line (O'Brien, 1984), is proposed. The statistic is shown to approximate the likelihood ratio test statistic for such alternatives (Kudô, 1963; Perlman, 1969). Its null distribution is a special case of the chi-bar-squared distribution, which allows critical values to be obtained. Such a…

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