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二元单非中心 t 分布的级数表示
This article presents a derivation of the probability density function and the cumulative distribution function of two correlated t statistics, for the central and singly noncentral case. The distribution of the ratios of means to standard deviations of a bivariate normal sample, is considered in particular.
双重非中心 t 分布的级数表示
This paper gives analytic expressions for the distribution function of t″, a doubly noncentral t-distribution, with v degrees of freedom and noncentrality parameters δ and λ, in series of Incomplete Beta and Hypergeometric (Gauss and Confluent) functions. Numerical values of Pr(t″ ≤t| ν, δ, λ) for v = 2 (1) 20, λ = 0 (2) 8, |δ| = 0 (1) 5, t = 0 and 1 are given in Table I.
双重非中心 t 分布的矩
This paper gives analytic expressions for the moments and recurrence relations for the first four raw moments of a doubly noncentral t-distribution with v degrees of freedom and noncentrality parameters δ and λ. Table I provides numerical values of these moments for v = 2 (1) 20, λ = 2 (2) 8 (4) 20 and any suitable δ. Two approximations to the t″-distribution, involving the moments, are considered.
局部无偏的 M 型检验
Summary In certain tests of hypotheses concerning more than one parameter, it is found that the criterion of unbiasedness cannot be satisfied. In such situations, it is proposed to make the test locally unbiased in a modified sense, termed Type M. Here the power surface in the parametric space does not always lie above the level of significance of the test. However, the mean value of the power, in a small neighbourhood of the null point, exceeds the significance level. This…