A probabilistic relation between the error estimates of physical quantities obtained by different methods

Authors

  • M.K. Abubekerov
  • N.Yu. Gostev

Keywords:

least-squares method
statistics
confidence interval
chi-square
confidence region method
error estimates
processing of observational data

Abstract

A distribution function for the ratio of the error estimates of physical quantities calculated using the confidence region method (based on the chi-square statistics) to the errors estimates calculated using the least-squares method is obtained. If the analytical form of this function is used, then the most probable values of the error estimates calculated by the confidence region method can easily be obtained using only the error estimates calculated by the least-squares method (without new observational data processing). Apart from a purely mathematical interest, this paper is of interest to experimenters involved in the processing of observational data, in particular, in the processing of astrophysical observations.


Published

2014-12-07

Issue

Section

Section 1. Numerical methods and applications

Author Biographies

M.K. Abubekerov

Lomonosov Moscow State University
• Senior Researcher

N.Yu. Gostev


References

  1. Уилкс С. Математическая статистика. М.: Наука, 1967.
  2. Черепащук А.М. Тесные двойные звезды. М.: Физматлит, 2013.
  3. Абубекеров М.К., Гостев Н.Ю., Черепащук А.М. Анализ кривых блеска затменных систем с экзопланетами. Система HD 209458 // Астрономический журнал. 2010. 87, № 12. 1199-1220.
  4. Абубекеров М.К., Гостев Н.Ю., Черепащук А.М. Оценка ошибок параметров в обратных параметрических задачах. Поиск потемнения к краю звезд в классических затменных системах // Астрономический журнал. 2009. 86, № 8. 778-806.
  5. Popper D.M. Error analysis of light curves of detached eclipsing binary systems // Astronomical Journal. 1984. 89, N 1. 132-144.
  6. Абубекеров М.К., Гостев Н.Ю., Черепащук А.М. Анализ кривых блеска затменных систем с экзопланетами. Система HD 189733 // Астрономический журнал. 2011. 88, № 12. 1139-1163.
  7. Lampton M., Margon B., Bowyer S. Parameter estimation in X-ray astronomy // Astrophysical Journal. 1976. 208. 177-190.