The use of Fourier series in the evaluation of probability distribution functions
作者:
Jimmie D. Woods,
Harry O. Posten,
期刊:
Communications in Statistics - Simulation and Computation
(Taylor Available online 1977)
卷期:
Volume 6,
issue 3
页码: 201-219
ISSN:0361-0918
年代: 1977
DOI:10.1080/03610917708812040
出版商: Marcel Dekker, Inc.
关键词: Fourier series expansions of distribution functions;evaluation of distribution functions
数据来源: Taylor
摘要:
In statistics, Fourier series have been used extensively in such areas as time series and stochastic processes. These series; however, to a large degree have been neglected with regard to their use in statistical distribution theory. This omission appears quite striking when one considers that, after the elementary functions, the trigonometric functions are the most important functions in applied mathematics. In this paper a procedure is developed for utilizing Fourier series to represent distribution functions of finite range random variables as Fourier series with coefficients easily expressible (using Chebyshev polynomials) In terms of the moments of the distribution. This method allows the evaluation of probabilities for a wide class of distributions. It is applied to the
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