Solar Physics

, Volume 250, Issue 1, pp 183–197 | Cite as

Modeling of Sunspot Numbers by a Modified Binary Mixture of Laplace Distribution Functions

Article

Abstract

This paper presents a new approach for describing the shape of 11-year sunspot cycles by considering the monthly averaged values. This paper also brings out a prediction model based on the analysis of 22 sunspot cycles from the year 1749 onward. It is found that the shape of the sunspot cycles with monthly averaged values can be described by a functional form of modified binary mixture of Laplace density functions, modified suitably by introducing two additional parameters in the standard functional form. The six parameters, namely two locations, two scales, and two area parameters, characterize this model. The nature of the estimated parameters for the sunspot cycles from 1749 onward has been analyzed and finally we arrived at a sufficient set of the parameters for the proposed model. It is seen that this model picks up the sunspot peaks more closely than any other model without losing the match at other places at the same time. The goodness of fit for the proposed model is also computed with the Hathaway – Wilson – Reichmann \(\overline{\chi}\) measure, which shows, on average, that the fitted model passes within 0.47 standard deviations of the actual averaged monthly sunspot numbers.

Keywords

Solar Activity Binary Mixture Solar Phys Sunspot Number Sunspot Cycle 

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References

  1. Anilkumar, A.K.: 2004, New Perspective for Analyzing the Breakup, Environment, Evolution, Collision Risk and Reentry of Space Debris Objects. Ph.D. thesis, Department of Aerospace Engineering, Indian Institute of Science, India. Google Scholar
  2. Balakrishnan, N., Nevzorov, V.B.: 2003, A Primer on Statistical Distributions, Wiley, Hoboken. MATHGoogle Scholar
  3. de Meyer, F.: 1981, Solar Phys. 70, 259. CrossRefADSGoogle Scholar
  4. Elling, W., Schwentek, H.: 1992, Solar Phys. 137, 155. CrossRefADSGoogle Scholar
  5. Fan, J., Yao, Q.: 2003, Nonlinear Time Series Nonparametric and Parametric Methods, Springer, New York. MATHGoogle Scholar
  6. Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 1994, Solar Phys. 151, 177. CrossRefADSGoogle Scholar
  7. Nordemann, D.J.R.: 1992, Solar Phys. 141, 199. CrossRefADSGoogle Scholar
  8. Sello, S.: 2001, Astron. Astrophys. 377, 312. CrossRefADSGoogle Scholar
  9. Sorenson, H.W.: 1980, Parameter Estimation – Principles and Problems, Marcel Dekker, New York. MATHGoogle Scholar
  10. Whitlock, D.: 2006, Orbital Debris Q. News 10(2), 4. Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Applied Mathematics DivisionVikram Sarabhai Space CentreThiruvananthapuramIndia

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