Calculation of Statistics Relating to Periodic Variation

J. J. Howarth

Giotto Loess Research Group, Geography Department, Leicester University, LE1 7RH, UK.

DOI: 10.4236/oalib.1100640                

Abstract

It is often necessary for astronomers to interpret observational data in terms of periodic variation, or an additive combination of periodic variations. This paper shows how statistics relating to periodic variation—the frequency, amplitude and phase - may be inferred from raw observational data and, just as importantly, it provides estimates for the accuracy of such statistics in terms of the observational error. Formulae are given to enable the extraction of these statistics, together with error bounds that apply. Their use is illustrated by synthetically derived data which also serve to demonstrate, by Monte-Carlo methods, the veracity of these formulae.

Keywords

Periodic Variation, Monte-Carlo, Statistical Estimation, Fourier Analysis, Variable Stars, Rotating Asteroids, Double Star Systems, Superhumps

Conflicts of Interest

The authors declare no conflicts of interest.

References

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