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논문 기본 정보
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- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & computing Journal of applied mathematics & computing 제19권 제1호
- 발행연도
- 2005.1
- 수록면
- 427 - 438 (12page)
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From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.
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