A generalised Emerson recurrence relation

Rayner, John; Thas, O.; De Boeck, B.

A generalised Emerson recurrence relation

journal contribution

posted on 2025-05-09, 03:50 authored by John RaynerJohn Rayner, O. Thas, B. De Boeck

The Emerson (1968, Biometrics 24, 695–701) recurrence relation has many important applications in statistics. However, the original derivation applied only to discrete distributions. In the following, a simple derivation is given that generalizes the Emerson recurrence relation to any distribution for which the necessary expectations exist. A modern application is outlined.

History

Journal title

Australian and New Zealand Journal of Statistics

Volume

50

Issue

3

Pagination

235-240

Publisher

Blackwell Publishing Asia

Language

en, English

College/Research Centre

Faculty of Science and Information Technology

School

School of Mathematical and Physical Sciences

Rights statement

This is the accepted version of the following article: Rayner, J. C. W.; Thas, O.; De Boeck , B. “A generalised Emerson recurrence relation” Australian and New Zealand Journal of Statistics Vol. 50, Issue 3, p. 235-240 (2008) which has been published in final form at http://dx.doi.org/10.1111/j.1467-842X.2008.00514.x

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Keywords

Hermite polynomials orthonormal polynomials spherical Legendre polynomials

A generalised Emerson recurrence relation

History

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School

Rights statement

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