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A generalized Emerson recurrence relation

JCW Rayner, Olivier Thas (UGent) and Bert De Boeck (UGent)
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Abstract
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.
Keywords
orthonormal polynomials, Hermite polynomials, spherical Legendre polynomials, SMOOTH TESTS, FIT

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Citation

Please use this url to cite or link to this publication:

Chicago
Rayner, JCW, Olivier Thas, and Bert De Boeck. 2008. “A Generalized Emerson Recurrence Relation.” Australian & New Zealand Journal of Statistics 50 (3): 235–240.
APA
Rayner, JCW, Thas, O., & De Boeck, B. (2008). A generalized Emerson recurrence relation. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 50(3), 235–240.
Vancouver
1.
Rayner J, Thas O, De Boeck B. A generalized Emerson recurrence relation. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS. 2008;50(3):235–40.
MLA
Rayner, JCW, Olivier Thas, and Bert De Boeck. “A Generalized Emerson Recurrence Relation.” AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 50.3 (2008): 235–240. Print.
@article{629295,
  abstract     = {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.},
  author       = {Rayner, JCW and Thas, Olivier and De Boeck, Bert},
  issn         = {1369-1473},
  journal      = {AUSTRALIAN \& NEW ZEALAND JOURNAL OF STATISTICS},
  keyword      = {orthonormal polynomials,Hermite polynomials,spherical Legendre polynomials,SMOOTH TESTS,FIT},
  language     = {eng},
  number       = {3},
  pages        = {235--240},
  title        = {A generalized Emerson recurrence relation},
  url          = {http://dx.doi.org/10.1111/j.1467-842X.2008.00514.x},
  volume       = {50},
  year         = {2008},
}

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