A DeMoivre-Laplace theorem of all orders of regularity

The DeMoivre-Laplace Theorem states that the binomial probability distribution B(N; 1/2) tends for N to infinity to the Gaussian distribution. We extend this theorem to the difference quotients of the family of the binomial distributions with varying N, showing that they converge to the correspondin...

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Bibliographic Details
Main Author: van den Berg, Imme (author)
Format: article
Language:eng
Published: 2008
Subjects:
Binomial distribution
DeMoivre-Laplace Theorem
Pascal Triangle
Gaussian distribution
difference quotients
discrete heat equation
nonstandard analysis
Online Access:http://hdl.handle.net/10174/1396
Country:Portugal
Oai:oai:dspace.uevora.pt:10174/1396
Description
Summary:The DeMoivre-Laplace Theorem states that the binomial probability distribution B(N; 1/2) tends for N to infinity to the Gaussian distribution. We extend this theorem to the difference quotients of the family of the binomial distributions with varying N, showing that they converge to the corresponding differential quotients of the time-dependent Gaussian distribution. The convergence holds for difference quotients of all order.

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