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Metrika

, Volume 24, Issue 1, pp 99–105 | Cite as

Statistical analysis of Fourier coefficients in a restricted harmonic dial

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Abstract

Due to the physical nature of certain periodic data, the harmonic dial points (the Fourier coefficients obtained from harmonic analysis of the data) are sometimes restricted to circular regions in the dial plane. It is proposed that a circular normal distribution (CND) truncated outside a circular region be used to describe the probabilistic behavior of the random phenomena. Recurrence relations for the population moments of a CND truncated outside a circular region are derived. These recurrence relations are used to obtain consistent asymptotically (jointly) normal estimators of the unknown parameters of the distribution. A numerical example based on the harmonic dial points representing the 27-day recurrence tendency of the daily international magnetic character-figureC i is given to illustrate the theory.

Keywords

Stochastic Process Probability Theory Economic Theory Harmonic Analysis Dial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Physica-Verlag Rudolf Liebing KG 1977

Authors and Affiliations

  • D. Dyer
    • 1
  1. 1.Department of MathematicsUniversity of Texas at ArlingtonArlington

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