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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0724103-114502 |
| Date | 24 July 2003 |
| Creators | Shiao, Z-C |
| Contributors | Mong-Na Lo Huang, Fu-Chuen Chang, Chin-San Lee |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0724103-114502 |
| Rights | unrestricted, Copyright information available at source archive |
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