Corrections for biases in slope estimation

Details Corrections for biases in slope estimation Corrections for biases in slope estimation

Feb 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985apj...289..457m&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 289, Feb. 15, 1985, p. 457-466.

Statistics

13

Bias, Error Analysis, Normalizing (Statistics), Radiant Flux Density, Slopes, X Ray Sources, Normal Density Functions, Significance

Scientific paper

The corrections to the estimated slope of the N(greater than S) relation and of the luminosity function due to Gaussian fluctuation are examined. A method is given for estimating the bias in the slope of the N(greater than S) relation when several flux-limited samples are combined. The bias in this case is always less than in the case of a single sample and can be extremely small. It is shown that the bias is zero when the measured uncertainties are proportional to the observed flux. The bias in the slope of a luminosity function is determined using similar methods and may be very small. These effects afford the opportunity to analyze flux-limited samples where the minimum significance level is less than 4 sigma, approaching 3 sigma.

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