Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986apj...310..334s&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 310, Nov. 1, 1986, p. 334-342.
Astronomy and Astrophysics
Astrophysics
29
Data Sampling, Distribution Functions, Poisson Density Functions, X Ray Sources, Background Noise, Bias, Error Analysis, Mathematical Models, Signal To Noise Ratios
Scientific paper
The slope determination of a power-law number flux relationship in the case of photon-limited sampling. This case is important for high-sensitivity X-ray surveys with imaging telescopes, where the error in an individual source measurement depends on integrated flux and is Poisson, rather than Gaussian, distributed. A bias-free method of slope estimation is developed that takes into account the exact error distribution, the influence of background noise, and the effects of varying limiting sensitivities. It is shown that the resulting bias corrections are quite insensitive to the bias correction procedures applied, as long as only sources with signal-to-noise ratio five or greater are considered. However, if sources with signal-to-noise ratio five or less are included, the derived bias corrections depend sensitively on the shape of the error distribution.
Maccacaro Tommaso
Schmitt Juergen H. M. M.
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