The Chebyshev-Hermite moments and their applications to asymptotic expansions (Q1600648)
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scientific article; zbMATH DE number 1756332
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Chebyshev-Hermite moments and their applications to asymptotic expansions |
scientific article; zbMATH DE number 1756332 |
Statements
The Chebyshev-Hermite moments and their applications to asymptotic expansions (English)
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16 June 2002
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Define the Chebyshev-Hermite moments of distribution \(P\) by \[ \theta_k= \theta_k(P)= \int^\infty_{-\infty} H_k(x) P(dx),\qquad k= 0,1,2,\dots, \] where \(H_k\) is the Chebyshev-Hermite polynomial of order \(k\). In this paper asymptotic expansions based on the Chebyshev-Hermite moments in the central limit theorem are derived. Explicit estimates of approximation errors are given.
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central limit theorem
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asymptotic expansions
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Chebyshev-Hermite polynomials
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0.8155691623687744
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0.8055049777030945
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