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定号二次型联合分布的近似AI 解读

Multidimensional Wilson-Hilferty transformations support Gaussian approximations to certain joint distributions of quadratic forms in jointly Gaussian variates. Central and noncentral joint distributions are studied and applications are noted. Parameters of the approximating distributions are given up to terms of order o(v −2) in the degrees of freedom v. Numerical studies validate using these approximations over a range of parameters for an essential subclass of the…

定号二次型联合分布的近似AI 解读

Multidimensional Wilson-Hilferty transformations support Gaussian approximations to certain joint distributions of quadratic forms in jointly Gaussian variates. Central and noncentral joint distributions are studied and applications are noted. Parameters of the approximating distributions are given up to terms of order o(v −2) in the degrees of freedom v. Numerical studies validate using these approximations over a range of parameters for an essential subclass of the…

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加权卡方变量之和的分布AI 解读

We consider distributions of quadratic forms of the type Qk = Σ k j = 1 cj (xj + aj )2, where the xj 's are independent and identically distributed standard normal variables, and where cj and aj are nonnegative constants. Exact significance points of Qk , for selected values of cj and all aj = 0, have been published for k = 2, 3, 4, and 5. We give significance points for k = 6, 8, and 10. We propose and assess two new approximations to Qk : (1) fitting a Pearson curve with…

最大复相关系数的选择：渐近情形AI 解读

Selection of t largest from among k independent multiple correlation coefficients, , is provided by a procedure with the property that the probability of a correct selection is not smaller than a preassigned P* whenever the t largest θ i (1) exceed each remaining θ i by a magnitude δ1, and, simultaneously, (2) each θ i is at least δ2 times as large as each remaining θ i . The separation thresholds, 0 < δ1 < 1 and δ2 > 1 are also preassigned. Several applications are…

定号二次型分布的高斯近似AI 解读

Let Qk = Σk j-1 cj(xj + aj)2 be a definite quadratic form in independent standardized Gaussian variables, xj, EQk = 01. The normalizing transformation (Qk/01)h is investigated, where h is determined by the first three moments of Qk. A new Gaussian approximation to the noncentral chi-square (x2) distribution is found for which the coefficient of skewness is smaller than a cube root transformation in the literature. Our transformation specializes to the cube root…

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