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Two-sample discrimination of Poisson meansThis paper presents a statistical test for detecting significant differences between two random count accumulations. The null hypothesis is that the two samples share a common random arrival process with a mean count proportional to each sample's exposure. The model represents the partition of N total events into two counts, A and B, as a sequence of N independent Bernoulli trials whose partition fraction, f, is determined by the ratio of the exposures of A and B. The detection of a significant difference is claimed when the background (null) hypothesis is rejected, which occurs when the observed sample falls in a critical region of (A, B) space. The critical region depends on f and the desired significance level, alpha. The model correctly takes into account the fluctuations in both the signals and the background data, including the important case of small numbers of counts in the signal, the background, or both. The significance can be exactly determined from the cumulative binomial distribution, which in turn can be inverted to determine the critical A(B) or B(A) contour. This paper gives efficient implementations of these tests, based on lookup tables. Applications include the detection of clustering of astronomical objects, the detection of faint emission or absorption lines in photon-limited spectroscopy, the detection of faint emitters or absorbers in photon-limited imaging, and dosimetry.
Document ID
19950037413
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Lampton, M.
(Univ. of California, Berkeley, CA United States)
Date Acquired
August 16, 2013
Publication Date
December 1, 1994
Publication Information
Publication: Astrophysical Journal, Part 1
Volume: 436
Issue: 2
ISSN: 0004-637X
Subject Category
Statistics And Probability
Accession Number
95A69012
Funding Number(s)
CONTRACT_GRANT: NAS5-30180
CONTRACT_GRANT: NAGW-3823
Distribution Limits
Public
Copyright
Other

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