Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...432..207w&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 432, no. 1, p. 207-212
Astronomy and Astrophysics
Astronomy
1
Astronomical Models, Brightness, Gamma Ray Astronomy, Gamma Ray Bursts, Mathematical Models, Power Series, Statistical Analysis, Statistical Distributions, Statistical Tests, Correlation, Gamma Ray Spectra, Luminosity, Normal Density Functions, Null Hypothesis, X Ray Spectra
Scientific paper
We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H0, that the distribution is a pure power law: F(x) varies as x-alpha. We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H0 that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distributions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than Cmax)) - log (Cmax) distribution.
Lubin Lori Maxine
Wijers Ralph A. M. J.
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