NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
Is a data set distributed as a power law? A test, with application to gamma-ray burst brightnessesWe 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, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -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 H(sub 0) 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 distriibutions 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 C(sub max))) - log (C(sub max)) distribution.
Document ID
19950040770
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Wijers, Ralph A. M. J.
(Princeton Univ. Observatory, Princeton, NJ, United States)
Lubin, Lori M.
(Princeton Univ. Observatory, Princeton, NJ, United States)
Date Acquired
August 16, 2013
Publication Date
September 1, 1994
Publication Information
Publication: Astrophysical Journal, Part 1
Volume: 432
Issue: 1
ISSN: 0004-637X
Subject Category
Astrophysics
Accession Number
95A72369
Funding Number(s)
CONTRACT_GRANT: NAG5-1901
Distribution Limits
Public
Copyright
Other

Available Downloads

There are no available downloads for this record.
No Preview Available