A Reduction Formula for Normal Multivariate Integrals

R. L. Plackett

doi:10.1093/biomet/41.3-4.351

January 1, 1954Biometrika

A Reduction Formula for Normal Multivariate Integrals

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Key Points

Derive an exact reduction formula that simplifies the evaluation of multivariate normal probability integrals by relating them to lower-dimensional integrals.
Differentiated the multivariate normal distribution function with respect to correlation coefficients between pairs of variables.
Constructed a differential relationship expressing higher-order multivariate normal integrals in terms of integrals of lower dimensions.
Derived Plackett's reduction identity linking partial derivatives of normal orthant probabilities directly to lower-order normal densities.
Provided an analytical framework allowing high-dimensional normal probabilities to be evaluated through sequential integration over correlation parameters.

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Implication

Theoretical analysis demonstrates a reduction identity for normal multivariate integrals, highlighting simplified computation of orthant probabilities across correlated dimensions.

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R. L. Plackett (1954) studied this question.

synapsesocial.com/papers/6a1df0499f4b7580a4ef8529 https://doi.org/10.1093/biomet/41.3-4.351

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A Reduction Formula for Normal Multivariate Integrals

Key Points

No abstract yet

Implication

Discussion

Cite This Study

A Reduction Formula for Normal Multivariate Integrals

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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