Clarification of the Use of Chi Square and Likelihood Functions in Fits to Histograms - INSPIRE

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Clarification of the Use of Chi Square and Likelihood Functions in Fits to Histograms

Steve Baker
(
- UCLA
)
,
Robert D. Cousins
(
- UCLA
)

Jul, 1983

21 pages

Published in:

Nucl.Instrum.Meth. 221 (1984) 437-442

DOI:

10.1016/0167-5087(84)90016-4

Report number:

UCLA-HEP-83-3

View in:

KEK scanned document

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Abstract: (Elsevier)

We consider the problem of fitting curves to histograms in which the data obey multinomial or Poisson statistics. Techniques commonly used by physicists are examined in light of standard results found in the statistics literature. We review the relationship between multinomial and Poisson distributions, and clarify a sufficient condition for equality of the area under the fitted curve and the number of events on the histogram. Following the statisticians, we use the likelihood ratio test to construct a general χ 2 statistic, χ λ 2 , which yields parameter and error estimates identical to those of the method of maximum likelihood. The χ λ 2 statist further useful for testing goodness-of-fit since the value of its minimum asymptotically obeys a classical chi-square distribution. One should be aware, however, of the potential for statistical bias, especially when the number of events is small.

STATISTICAL ANALYSIS
MATHEMATICAL METHODS

References(36)

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