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非中心 Wishart 矩阵初等对称函数期望猜想的证明AI 解读

This paper provides proof of conjectures about the expected values of the $j$th elementary symmetric function of the roots (i.e. $E(\operatorname{tr}_j A)$) of a non-central Wishart matrix. Utilizing this result we have obtained computationally convenient formula for the expected value of the $j$th elementary symmetric function of the roots of central positive definite quadratic form in matrix argument.

均方相邻差一半的分布AI 解读

A convenient convergent method of computing the distribution function of half the mean square successive difference based on the Laguerre polynomial representation is obtained. This method does not require any use of quadrature formulae in computing probabilities and is suitable for digital computers for any linear combination of chi-squared variables with positive weights.

相邻差均方的一半的分布AI 解读

A convenient convergent method of computing the distribution function of half the mean square successive difference based on the Laguerre polynomial representation is obtained. This method does not require any use of quadrature formulae in computing probabilities and is suitable for digital computers for any linear combination of chi-squared variables with positive weights.