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A generalised Emerson recurrence relation

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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.

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  1. 1.
    DOI - Is published in https://doi.org/10.1111/j.1467-842X.2008.00514.x
  2. 2.
    ISSN - Is version of https://portal.issn.org/resource/ISSN/1369-1473

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 polynomialsorthonormal polynomialsspherical Legendre polynomials

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