Computer algebra in probability and statistics
作者:
W. S. Kendall,
期刊:
Statistica Neerlandica
(WILEY Available online 1993)
卷期:
Volume 47,
issue 1
页码: 9-25
ISSN:0039-0402
年代: 1993
DOI:10.1111/j.1467-9574.1993.tb01403.x
出版商: Blackwell Publishing Ltd
关键词: Brownian motion;computer algebra;graph equivalence problem;invariant Taylor series;Itǒ formula;itovsn3;ito procedures;Lévy stochastic area;MACSYMA;Maple;Mathernatica;REDUCE;semimartingale;statistical asymptotics;statistical yoke geometry;stochastic calcul
数据来源: WILEY
摘要:
This paper discusses the uses of computer algebra within statistics and probability. A distinction is drawn between the use of computer algebra packages tosupportinvestigations, by performing calculations, ankl their use toimplement structure;to build in elements of a theory (such as stochastic calculus or the Taylor string theory of Barndorff Nielsen and others) as a preliminary to research investigations. Brief surveys are given of instances in the literature of use of computer algebra in probability and statistics. Two examples of implementations of structure are discussed, both drawn from the author's own work with the computer algebra package REDUCE. One is a simple demonstration using moments of the Poisson distribution. The other isitovsn3, an implementation of the semimartingale stochastic calculus. It is described howitovsn3may be used to derive the characteristic function of the Lévy stochastic area, following a proof due to S. Janson. Prospects for future work and for work in progress are discussed
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