Polynomial-Gaussian vectors and polynomial-Gaussian processes

• Autorzy: Plucińska A. , Bisińska M.
• Języki publikacji: EN

Abstrakty

EN

The density of a d-dimensional polynomial-Gaussian distribution (PGDd) 5 the product of a non-negative polynomial and a Gaussian density. The density of a (PGDd) has many properties similar to a rf-dimensional Gaussian distribution (GDd), but one-dimensional marginal distributions of (PGDd) are (PGD1). Analogously one-dimensional densities of a polynomial-Gaussian process (PGP) are (PGD1). We investigate the differences and similarities between the Gaussian and non-Gaussian cases.

Słowa kluczowe

EN

polynomial-Gaussian distribution; Gausian density

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 2
• Strony: 359--374
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Plucińska A.

• Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warsaw, Poland

autor

Bisińska M.

• Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warsaw, Poland

Bibliografia

• [1] M. Evans and T. Swartz (1994), Distribution theory and inference for polynomial-normal densities, Comm. Stat., Theory Methods 23 (4), 1123-1148.
• [2] N. Johnson and S. Kotz (1972), Distributions in Statistics: Continuous Multivariate Distributions, John Wiley, New York.
• [3] R. S. Liptser and A. N. Shiryaev (1978), Statistics of Random Processes, Springer, New York.
• [4] E. Lukacs (1970), Characteristic Functions, Griffin, London.
• [5] A. Plucińska (2001), Composition and Decomposition of Polynomial-Normal Distributions, Janos Bolyai Math. Society, Proc of "Fourth Hungarian Colloquium on Limit Theorems of Probability and Statistics", (to appear in 2001).
• [6] A. Plucińska (1999), Some properties of polynomial-normal distributions associated with Hermite polynomials, Demonstratio Math. 32, No 1, 195-206.
• [7] A. P. Prudnikov, Y. A. Brychkov and O. I. Marichev (1983), Integrals and Special Functions, Nauka, Moscow (in Russian).
• [8] A. N. Shiryaev (1996), Probability, Springer, New York.