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In statistics, the Cunningham function or Pearson–Cunningham function ωm,n(x) is a generalisation of a special function introduced by and studied in the form here by . It can be defined in terms of the confluent hypergeometric function U, by The function was studied by Cunningham in the context of a multivariate generalisation of the Edgeworth expansion for approximating a probability density function based on its (joint) moments. In a more general context, the function is related to the solution of the constant-coefficient diffusion equation, in one or more dimensions.

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  • Cunningham function
  • 坎宁安函数
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  • 坎宁安函数又称为皮尔逊-坎宁安函数(Pearson-Cunningham function)是英国数学家坎宁安在1908年首先研究的特殊函数,,定义如下: 其中U为特里科米函数。 坎宁安在是在用多變數擴展的埃奇沃斯級數,依機率密度函數的矩來近似機率密度函數時用到坎宁安函数,坎宁安函数和一維或多維常係數的擴散方程有關 坎宁安函数是下列微分方程的解
  • In statistics, the Cunningham function or Pearson–Cunningham function ωm,n(x) is a generalisation of a special function introduced by and studied in the form here by . It can be defined in terms of the confluent hypergeometric function U, by The function was studied by Cunningham in the context of a multivariate generalisation of the Edgeworth expansion for approximating a probability density function based on its (joint) moments. In a more general context, the function is related to the solution of the constant-coefficient diffusion equation, in one or more dimensions.
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  • In statistics, the Cunningham function or Pearson–Cunningham function ωm,n(x) is a generalisation of a special function introduced by and studied in the form here by . It can be defined in terms of the confluent hypergeometric function U, by The function was studied by Cunningham in the context of a multivariate generalisation of the Edgeworth expansion for approximating a probability density function based on its (joint) moments. In a more general context, the function is related to the solution of the constant-coefficient diffusion equation, in one or more dimensions. The function ωm,n(x) is a solution of the differential equation for X: The special function studied by Pearson is given, in his notation by,
  • 坎宁安函数又称为皮尔逊-坎宁安函数(Pearson-Cunningham function)是英国数学家坎宁安在1908年首先研究的特殊函数,,定义如下: 其中U为特里科米函数。 坎宁安在是在用多變數擴展的埃奇沃斯級數,依機率密度函數的矩來近似機率密度函數時用到坎宁安函数,坎宁安函数和一維或多維常係數的擴散方程有關 坎宁安函数是下列微分方程的解
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