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Title: MAXIMUM-LIKELIHOOD ESTIMATION OF THE SLOPE FROM NUMBER-FLUX-DENSITY COUNTS OF RADIO SOURCES.

Authors:
; ;
Publication Date:
Research Org.:
Cornell-Sydney Univ. Astronomy Center, Ithaca, N. Y.
Sponsoring Org.:
USDOE
OSTI Identifier:
4083074
NSA Number:
NSA-25-007014
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophys. J. 162: 405-10(Nov 1970).; Other Information: Orig. Receipt Date: 31-DEC-71
Country of Publication:
Country unknown/Code not available
Language:
English
Subject:
N32130* -Physics-Astrophysics-Quasi-stellar, Radio & X- Ray Sources; COSMIC RADIO SOURCES; DISTRIBUTION; ERRORS; COSMIC RADIO SOURCES/number-flux-density counts of, maximum-likelihood estimation of slope from,, (E)

Citation Formats

Crawford, D.F., Jauncey, D.L., and Murdoch, H.S.. MAXIMUM-LIKELIHOOD ESTIMATION OF THE SLOPE FROM NUMBER-FLUX-DENSITY COUNTS OF RADIO SOURCES.. Country unknown/Code not available: N. p., 1970. Web. doi:10.1086/150672.
Crawford, D.F., Jauncey, D.L., & Murdoch, H.S.. MAXIMUM-LIKELIHOOD ESTIMATION OF THE SLOPE FROM NUMBER-FLUX-DENSITY COUNTS OF RADIO SOURCES.. Country unknown/Code not available. doi:10.1086/150672.
Crawford, D.F., Jauncey, D.L., and Murdoch, H.S.. Thu . "MAXIMUM-LIKELIHOOD ESTIMATION OF THE SLOPE FROM NUMBER-FLUX-DENSITY COUNTS OF RADIO SOURCES.". Country unknown/Code not available. doi:10.1086/150672.
@article{osti_4083074,
title = {MAXIMUM-LIKELIHOOD ESTIMATION OF THE SLOPE FROM NUMBER-FLUX-DENSITY COUNTS OF RADIO SOURCES.},
author = {Crawford, D.F. and Jauncey, D.L. and Murdoch, H.S.},
abstractNote = {},
doi = {10.1086/150672},
journal = {Astrophys. J. 162: 405-10(Nov 1970).},
number = ,
volume = ,
place = {Country unknown/Code not available},
year = {Thu Jan 01 00:00:00 EST 1970},
month = {Thu Jan 01 00:00:00 EST 1970}
}
  • The application of the method of maximum likelinood to the determination of the slope of the number- flux-density relationship is extended to include the presence of experimental errors in the flux-density measurements. It is shown that these experimental errors have a significant effect on the number counts at higher natios of flux density to error than is often recognized. The case of noise-limited fiux-density measurements is treated in some detail, and it is found that, provided the lower limit of a survey is chosen to be at least five times the rms noise, the enhancement in the source density asmore » a function of fiux density can be readily calculated. For the case of significart confusion errors in the flux-density measurements the importance of a Monte Carlo approach is emphasized. Several methods that have been used previously are discussed and a number of shortcomings noted. (auth)« less
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  • 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 ormore » 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. 12 references.« less