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The numerical evaluation of a class of integrals. II

Published online by Cambridge University Press:  24 October 2008

S. C. Das
S. C. Das
Affiliation:
Australian National University Canberra, A.C.T.
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Extract

Consider the integral

where x1, x2, …, xN are jointly distributed in a multivariate normal distribution f(x1, x2, …, xN) with (pij) as the correlation matrix. The integral has been expressed in an infinite series of tetrachoric functions for N≥2. The infinite series is not only complicated, but also is very slowly convergent and is consequently not of much practical use. Plackett (8) obtains a reduction formula for expressing normal integrals in four variates as a finite sum of single integrals of tabulated functions. These integrals have then to be evaluated by a rather awkward numerical quadrature.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 3 , July 1956 , pp. 442 - 448
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

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