School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan NSW 2308, Australia. e-mail: John.Rayner@newcastle.edu.au
A GENERALIZED EMERSON RECURRENCE RELATION
Article first published online: 8 SEP 2008
© 2008 Australian Statistical Publishing Association Inc.
Australian & New Zealand Journal of Statistics
Volume 50, Issue 3, pages 235–240, September 2008
How to Cite
Rayner, J. C. W., Thas, O. and De Boeck, B. (2008), A GENERALIZED EMERSON RECURRENCE RELATION. Australian & New Zealand Journal of Statistics, 50: 235–240. doi: 10.1111/j.1467-842X.2008.00514.x
- Issue published online: 8 SEP 2008
- Article first published online: 8 SEP 2008
- Hermite polynomials;
- orthonormal polynomials;
- spherical Legendre polynomials
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.