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Methods of periodicity analysis - Relationship between the Rayleigh analysis and a maximum likelihood methodFor periodicity analysis of occurrence rates of discrete events, one can use the maximum likelihood method or the 'Rayleigh analysis'. In a maximum likelihood analysis using a sinusoidal distribution, one tries various values of amplitude A and phase angle Theta(0) of the distribution function. We show that these two methods are essentially equivalent to one another in spite of their different mathematical origins. Using the Rayleigh analysis, therefore, we can simply calculate A and Theta(0) which maximize the likelihood. Using the cumulative nature of the logarithmic likelihood, we can identify time intervals during which the periodicity is in operation. When a periodicity operates only in certain time intervals, it is important to identify these intervals. Mathematically, the above technique is applicable only to discrete events. However, with slight modifications we can apply this technique to general cases - periodicity analysis of measurements of continuously varying quantities.
Document ID
19930026502
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Bai, T. (Stanford Univ. CA, United States)
Date Acquired
August 15, 2013
Publication Date
October 1, 1992
Publication Information
Publication: Astrophysical Journal, Part 1
Volume: 397
Issue: 2
ISSN: 0004-637X
Subject Category
ASTROPHYSICS
Funding Number(s)
CONTRACT_GRANT: NAS8-37334
CONTRACT_GRANT: N00014-85-K-0111
CONTRACT_GRANT: NAGW-2265
CONTRACT_GRANT: N00014-89-J-1024
Distribution Limits
Public
Copyright
Other