Integral identities for random variables
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Authors
Rockower, Edward B.
Subjects
characteristic functions, generating functions,
transforms, moments, identities
Advisors
Date of Issue
1986-10
Date
1986-10
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
Using a general method for deriving identities for random variables, the author finds a number of new results involving characteristic functions and generating functions. The method is simply to promote a parameter in an integral relation to the status of a random variable and then take expected values of both sides of the equation. Results include formulas for calculating the characteristic functions for sq x, square root of x, 1/x, sq x + x, sq R = sq x + sq y, etc. in terms of integral transforms of the characteristic functions for x and (x,y), etc. Generalizations to higher dimensions can be obtained using the same method. Expressions for inverse/ fractional moments, E(n ), etc. are also presented, demonstrating the method
Type
Technical Report
Description
Series/Report No
Department
Operations Research
Identifiers
NPS Report Number
NPS55-86-017
Sponsors
Prepared for: Commander, Space and Naval Warfare Systems Command
Washington, D.C.
Funder
N0003986WRDJ850
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.