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Computation of moment generating and characteristic functions with Mathematica

Mathematica is an extremely powerful and flexible symbolic
computer algebra system that enables the user to deal with
complicated algebraic tasks. It can also easily handle the
numerical and graphical sides. One such task is the derivation of
moment generating functions (MGF) and characteristic functions
(CF), demonstrably effective tools to characterize a distribution.
In this paper, we define some rules in Mathematica to help in
computing the MGF and CF for linear combination of independent
random variables. These commands utilizes pattern-matching code
that enhances Mathematica's ability to simplify expressions
involving the product of algebraic terms. This enhancement to
Mathematica's functionality can be of particular benefit for MGF
and CF. Applications of these rules to determine mean, variance
and distribution are illustrated for various independent random
variables.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0724103-114502
Date24 July 2003
CreatorsShiao, Z-C
ContributorsMong-Na Lo Huang, Fu-Chuen Chang, Chin-San Lee
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0724103-114502
Rightsunrestricted, Copyright information available at source archive

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