Calculation of Statistics Relating to Periodic Variation
Author(s)
J. J. Howarth
Affiliation(s)
Giotto Loess Research Group, Geography Department, Leicester University, LE1 7RH, UK.
Giotto Loess Research Group, Geography Department, Leicester University, LE1 7RH, UK.
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.
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
Periodic Variation, Monte-Carlo, Statistical Estimation, Fourier Analysis, Variable Stars, Rotating Asteroids, Double Star Systems, Superhumps
Cite this paper
Howarth, J. (2014) Calculation of Statistics Relating to Periodic Variation. Open Access Library Journal, 1, 1-8. doi: 10.4236/oalib.1100640.
Howarth, J. (2014) Calculation of Statistics Relating to Periodic Variation. Open Access Library Journal, 1, 1-8. doi: 10.4236/oalib.1100640.
References
[1] Howarth, J.J. and Greaves, J. (2001) Amplitude and Phase Changes in the Light Curves of Long-Period Variables. Monthly Notices of the Royal Astronomical Society, 325, 1383-1388.
http://dx.doi.org/10.1046/j.1365-8711.2001.04489.x [2] Koen, C. (1990) Significance Testing of Periodogram Ordinates. Astrophysical Journal, 348, 700.
http://dx.doi.org/10.1086/168277 [3] Margenau, H. and Murphy, G.M. (1968) The Mathematics of Physics and Chemistry. Van Nostrand Reinhold, New York. [4] Cohen, A.M. (1973) Numerical Analysis. McGraw-Hill, New York. [5] Kovacs, G. (1981) Frequncy Shift in Fourier Analysis. Astrophysics and Space Science, 78, 175-188.
http://dx.doi.org/10.1007/BF00654032 [6] Percy, J.R. and Polano, S. (1998) Pulsation Modes in M Giants. In: Bradley, P.A. and Guzik, J.A., Eds., A Half-Century of Stellar Pulsation Interpretations: A Tribute to Arthur N Cox, Astronomical Society of the Pacific Conference Series, 135, 249. [7] Mattei, J.A., Foster, G., Hurwitz, L.A., Malatesta, K.H., Willson, L.A. and Mennessier, M.-O. (1997) Classification of Red Variables. In: Battrick, B., Ed., Proceedings of the ESA (European Space Agency) Symposium, ESA, Noordwijk, ESA SP-402, 269. [8] Hammersley, J.M. and Handscomb, D.C. (1964) Monte-Carlo Methods. Springer Netherlands
http://dx.doi.org/10.1007/978-94-009-5819-7
[1] Howarth, J.J. and Greaves, J. (2001) Amplitude and Phase Changes in the Light Curves of Long-Period Variables. Monthly Notices of the Royal Astronomical Society, 325, 1383-1388.
http://dx.doi.org/10.1046/j.1365-8711.2001.04489.x [2] Koen, C. (1990) Significance Testing of Periodogram Ordinates. Astrophysical Journal, 348, 700.
http://dx.doi.org/10.1086/168277 [3] Margenau, H. and Murphy, G.M. (1968) The Mathematics of Physics and Chemistry. Van Nostrand Reinhold, New York. [4] Cohen, A.M. (1973) Numerical Analysis. McGraw-Hill, New York. [5] Kovacs, G. (1981) Frequncy Shift in Fourier Analysis. Astrophysics and Space Science, 78, 175-188.
http://dx.doi.org/10.1007/BF00654032 [6] Percy, J.R. and Polano, S. (1998) Pulsation Modes in M Giants. In: Bradley, P.A. and Guzik, J.A., Eds., A Half-Century of Stellar Pulsation Interpretations: A Tribute to Arthur N Cox, Astronomical Society of the Pacific Conference Series, 135, 249. [7] Mattei, J.A., Foster, G., Hurwitz, L.A., Malatesta, K.H., Willson, L.A. and Mennessier, M.-O. (1997) Classification of Red Variables. In: Battrick, B., Ed., Proceedings of the ESA (European Space Agency) Symposium, ESA, Noordwijk, ESA SP-402, 269. [8] Hammersley, J.M. and Handscomb, D.C. (1964) Monte-Carlo Methods. Springer Netherlands
http://dx.doi.org/10.1007/978-94-009-5819-7